Oh wow I can make one of these. anyways I want to know what YOU thinks makes a good level, because I'm not really sure and have decided to crowd source it? so again, what do YOU thinks goes into a good level?
So the answers to that question (and other people please post too, including students!!) could fill VOLUMES of books. There's no "magic bullet" and that's why the "perfect game" doesn't exist - although there are certainly games/levels that individual people think are perfect, if it truly was "the perfect level" I think there'd be universal agreement that "that's the one!".
Having said that - there's also two different contexts. The perfect level and the perfect vertical slice are potentially two very different things because they're designed differently. A level is GENERALLY meant to be part of a sequence, so it should build toward the next goal while building on the previous - and that "building" should involve decisions like difficulty curve, story progression, intensity curve, mechanics introduction, etc. Like a heart, different ones are "stronger" in each level and some rest (resting in this case doesn't mean "stop", but it means maybe slower) - for instance a portion of my game that is particularly intense in terms of gameplay/difficulty might be a good time to give the story/narrative a rest because I don't want the player *SO FOCUSED* on the action that they miss a vital piece of the story. On the other hand, I might choose to ramp up the intensity on all three simultaneously to create a REALLY intense sequence, but if I do that I DEFINITELY would choose to give a player a break after that.
In my opinion Portal is kinda a masterclass in level design. There's a very deep, rich progression for mechanics introduction so it doesn't feel overwhelming, and although the story isn't particularly deep it's played out well. Much of the story beats occur while you're either navigating hallways or still getting your bearings in a level, and the most substantial part of the story (your eventual betrayal) happens while you're on a moving platform waiting so you're not really doing ANYTHING. At times the game gives you some fairly intense action but then it pauses a second and lets you breathe after.
In a vertical slice you don't get that kind of time - you're looking at gameplay in the scope of 10 minutes or so (tops - most games in the contest are closer to five) - so you're trying to make a more complete experience in shorter time. That means your story is, by necessity, going to need to be told in an accelerated timeframe and you want your level to EFFECTIVEY demonstrate everything you've put into the game - but neither should be overwhelming. There's a few good ways to accomplish this subtly and the more specific answers depend on the exact type of game you're going to make (In my head right now I'm making a platformer with some different powerups), but here's some strategies that you can adapt for your specific games. I'm going to talk mechanics specifically but these same ideas could be adapted to other contexts as well.
In metroid (NES) one of the first powerups you get is the maru mari. To help introduce it, getting TO it is very easy and doesn't require any powerups. Getting AWAY from it once you get far enough is impossible - you basically fall off a cliff that is impossible to get back up, but you can use the maru to go UNDER the blocks to get back. That forces your hand to finish getting the item, and insures that you are able to USE it before you're allowed out of the immediate area. For that first encounter, there is potentially an enemy present (if you didn't kill it or if it respawned) but this enemy is very easily killed or avoided (it's slow) - this isn't a very intense moment difficulty-wise and gives you a chance to figure out the mechanics of your new item.
Another thing metroid does well in level design (and I think it's worth noting here that although I'm using it as my examples, there's also a lot of flaws in their design, so it's by no means a game I'd personally want to 100% emulate in my own design) is that it has deliberately blocked progression points that you can SEE. VERY early in the game you see areas where the platforming goes up or down, but you've got no way of accessing those areas - yet. So from almost your first moments in the game you're aware that 1) These other places exist, but 2) They're inaccessible at this time so 3) I must need some other item or trick to get past them. Later when I discover bombs, I'm able to use them to open those areas. A similar technique blocks me using the Red Doors - I've learned by now that blue doors react to my normal bullets, but red doesn't - so I can assume I need to shoot it with something more powerful *BUT* I need to find a more powerful weapon first (missiles).
Those mechanics preserve the "open world" feel of metroid, but also don't allow a player to get into an area that they aren't ready for yet (the enemy difficulty and/or platforming are too high, or items might be needed you don't have yet). Although players MIGHT be able to approach things out of order, it usually takes a sufficiently advanced player to do so, one who has generally learned the correct way to do things but is looking for a self-imposed challenge by doing it in a way they know is "wrong" (like players who try to beat zelda without using a sword, etc).
Other misc tips:
Everything in the level should be deliberate. If you can't tell me "why is that there", it probably shouldn't be.
Walking isn't gameplay. I might have a short corridor to give my player a breather but long sequences of walking? What purpose did that serve?
Since your gameplay is so short, your story needs to be too. Distill it down to its most basic elements. Think you can't tell a story that fast? Watch the intro of any pixar movie (either the shorts or the actual introduction). Watch the opening sequence of "up" (3 minutes, 2 seconds) and tell me you can't tell a complete story in a short timeframe.
If it's not shown in the level, it didn't happen. We don't need to generate 50 pages of backstory for a 3 minute event - and the only part of the story we care about is the part we see.
For the love of god don't have a 10 screen opening text sequence that explains every intricate detail of your story. Three sentences, tops. SHOW DON'T TELL. Again, we only care about the parts we get to play. And if you're going to insist on doing it, at least let us click through it. When I'm evaluating (I'm not a panelist on this one, but I've been one in similar contests) I'm usually going to play at least once to get a feel, I'll probably screw up and restart at least once, and I'm going to do a slow replay or two after that while I'm trying to refine my notes. If I have to sit through 15 minutes of story introduction that many times that I can't skip, I hate you, I hate your game, and I'm actively wishing for your failure. Okay, so that last bit was a slight exaggeration... but *slight*.
Don't make a "rage" game. Especially with a theme like perseverance, it's easy to want to make a "trial and error" game with absurd levels of difficulty. The only person who enjoys rage games is the person who makes them. Making a quality one (like Dark Souls) requires very specific design philosophy and even with THAT there's a reason there are so very few successful ones. Making your players angry isn't a good way of scoring points with your panel.
At the same time - I want a little challenge. If you give me candyland (it's not even a "game", there's literally zero challenge or player agency) I'm gonna get annoyed because I want a game. If you have to choose it's probably better to do a slightly easier thing than a harder thing, but keep in mind that while YOU'VE (hopefully) played your game hundreds of times, we've never played it and don't have the reflexes in it you do. Hand your game to someone who DOESN'T know the game, don't guide them AT ALL and see how they play it. Are they navigating obstacles the way you want them to? Are they able to discover what you want them to discover? Is it too easy for them? etc.
Your panel is all industry people - they know how to play games (you can say "wasd controls" and we know what that means, but DEFINITELY tell us what the controls are!) but they might not be action junkies or platformer experts. For example, I personally don't tend to play "twitch" games that require fast reflexes - I prefer to play slower games that require you to think through your steps. When I'm evaluating a platformer I'm thinking "If I played platformers regularly, would I enjoy this", but I don't have highly honed platforming reflexes so I can't beat levels designed for Platforming Players. Push me a bit but don't overwhelm.
Strictly opinion, and some of the panelists may disagree with me here (it's a pretty hotly debated topic amongst developers), but IMHO if you have to decide between gameplay and story, gameplay wins. Unless you have a story in mind and a specific gameplay that's going to accomplish it (rare), a better approach is to start developing the game's mechanics and gameplay and see what story emerges from it - if any. A good game can exist without story (see: tetris, and even the original zelda was fairly thin story-wise... rescue the princess by collecting All The Things? One item to rule them all? How innovative..) but a good game doesn't happen without good gameplay/mechanics. Good gameplay can salvage a bad story, but it's very hard for a good story to salvage bad gameplay.
Having said that: Story is enriching. I generally won't personally touch a product unless I can craft story with it (even if it's not a "deep" story), if we think about our very favorite games there's generally some layer of story - and there's specifically a story award *AND* a narrative director on our panel. So while you CAN win Game of the Year without story... it's a lot easier with one.