Hey gliebetronics - sorry for the error! It turns out that it wasn't uploading all the files I thought it was, so some stuff was missing. I've re-uploaded the game as a zip containing all the necessary files, so if you re-download it you should be all good. Thanks for your patience while I figure out the itch.io interface!
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I can't speak for the devs personally, but this is customarily done with a vertex shader, as explained in this video (just a random google result, I'm not affiliated with this guy in any way)
The short version is that the world probably isn't curved (since, as you pointed out, collision would be more complicated and costly) but rather the shader bends your perception of the world like a funhouse mirror. Hope that helps!