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Okay, I played v1.02 as well, but I didn't notice any checkpoint system whatsoever. If you don't want to add checkpoints, then perhaps you can make it more fun to replay the same parts over and over again.

This time I noticed that there was a secret room (before meeting other creature) and that there was this button behind a door that I couldn't get to (near moving platform). Maybe there can be secret paths that you only know about once you clear a certain part.

Yeah, those are shortcuts that you open from the other side so you bypass some of the rooms you alrady finished. This imo suits it much more then just simple checkpoints.