(I am now in a rush to test as many games as possible to help, so please do not mind the cursory reviewing style.)
[testing the navigator version; which is up to date? Not sure]
Controls are layout-independent, great! :) (I have an AZERTY keyboard)
Movement is a bit fast and "stiff"/unforgiving! In particular, not sure what makes the square unstick from a wall… Ah, I think this is because you have to keep moving towards the wall; you could also "stick" it, and let the player unstick with a single press (this is debatable). (Reading "The speed is in my opinion what makes the game fun.": I agree that the speed has a funny effect here, actually, but the "stiffness" of some controls, including wall jump, could probably be dealt with.)
I think some sounds would help getting the action and adding life! Such a game with simple geometric shapes would go well with sfxr, for example. :)
4th screen: I thought going to the right again, but lost!
I like how you can the your trajectory (purple line). :)
Managed level 1: so, that was the green "door", got it. X)
Level 2: the two tints of red for regular and deadly platform are too close, I think!! I would either make the colours more different, or add something to the deadly ones so they stand out (a texture/drawing, or an outline, or blinking…).
Oh, and the greenish (transparent?) ones are teleporters! Reminded me of the exit from level 1; same colour-related advice here.
And what are you supposed to do next?? I managed to teleport and then get on the white rectangle, but… I am in a sorry situation!
Trying level 3: OH, you HAVE TO finish level 2 first!! <:o
Back to level 2: going right, maybe? YES! So, the white rectangle was in fact a BLOCKING WALL; I would advise making it go to the top of the screen, so that silly individuals like me not be tempted to jump on it. X) And maybe add an arrow on the right?
3rd screen: moving left makes you teleport back to the 2nd screen and lose… :s
3rd screen: really no time to think or even see if you are moving / pressing a key when entering!
Beat level 2! :) Died some times just before the end; SUGGESTION: remove the teleporting capacity of the receiving teleporter altogether. As this is apparently a game with no turning back (except if you intend such levels), it makes sense, and would spare many deaths to the player.
Beat level 3! :D Way faster then the two previous ones! By the way, what is the difference between blue and green teleporters?
Takeaway: GOOD concept, totally in line with the constraint, BUT some playability and implicit indication/understanding issues can hinder the player — the latter should be easy to solve! :) Also got better at it through die-and-retry training, and found it more and more pleasable, while the very start was a bit painful! You are thrown right into the action with no time to think; a less steep difficulty curve would help, like a tutorial level, for example ("I'll add some tutorial at the start" -> so, already planned :)).
This nice fast-paced concept can definitely go somewhere, it was a pleasant time. :)