I hadn't read the xkcd comic before this--that's a great strip to make a game after! I love the idea of exploring the world of that comic strip in a platformer.
Since pretty much all the content from your game is from the xkcd comic, I won't review that. I will review the mechanics and how they're implemented, and the design you used in your game. So here we go! :)
First off, love the fact that you have the xkcd strip itself as an intro. The fade in speed is perfect. And you use fade-in for all the dialogue, too, which is great! Also, love that you included a map (though a player wouldn't know there was one if they never pause) and that you can continue your game where you left off.
But the main element of the game, the exploration, feels off. The run speed is way too fast and the animation that goes with it is rather jilted. And because of the fast run speed, the screen can barely scroll to catch up as I explore. Also the jump is quite high.
I do understand that you might've wanted to make the run speed fast so a player could explore the huge area in a reasonable amount of time. But personally I think the run is way to fast and almost forces a player to take in the area too quickly, or else explore it in quick little bursts; to me, I read the xkcd comic this was based on as an opportunity to slow down and explore its world, and this game does not capture that essence. Not helping is the fact that I clipped on platforms and edges a lot; I found myself walking on the air at one point for some reason as well, and when I was at the tree with the tire swing I pressed down and slowly went into the ground.
Overall, I enjoyed my time here. Would love to see a more polished version after the jam is over. Great job on this. :)