Hi Radu!
Your game looks very nice, it's visually pleasing. I understand you did this all yourself? Great job! I liked how it was easy to distinguish which islands you have visited and which ones you haven't.
The feel of the game was nice once you've gotten the hang of the mechanics. The latter is the largest issue I have with it though. The immediate double jump doesn't feel very intuitive. In most games a double jump is used to get extra height, either at the apex of your jump or once you see that you won't be able to reach it. Having to press space again immediately after having pressed jump feels very weird. Also it's not explained in the game. I don't feel a game should ever rely on external resources to teach you how it works, unless it's a boardgame.
Besides that, the teleportation thing didn't work well in my opinion. Sure it worked well, if you'd get the center orb as last, but if you'd pick it up later you would have too much momentum left from your jump and you would quickly die in the second level. I think this could be circumvented by placing the players on the starting platform again. Even if they are holding down keys if they see the starting area they are already familiar with they know they can stop holding down the button, reorient themselves, and then jump into the thick of it again.
Also, since your game is placed in a void with no underground or anything, sometimes it was very unclear which platforms you could jump to, this was less a problem in the second level, but it was especially frustrating in the second level.
Overall your game was good!