A game can be appealing for various reasons, like if it has a new game mechanic or is challenging or tells an engaging story. This game's main appeal is the storytelling (I wouldn't call it a new game mechanic since the underlying platforming is fairly standard), so if you'd like to continue developing games along this concept my biggest recommendation would be to focus on developing as epic and engaging of a story as possible. People are loving the interactivity with the character's ability to change the storyline, so that should also be included. One natural extension of those two put together would be to have the story behind the game initially be somewhat mysterious and obfuscated but gradually revealed as puzzles are solved, although I'm sure there are many other good approaches you could take.
Aside from the storytelling, the other basic aspects of making an enjoyable platformer would still apply - making sure that the pace of the game is appropriate (in this case make the story unfold at an appropriate pace given the average person's playthrough speed, and if there's any backtracking involved then don't let it get too tedious), that all the physics and collision detection is sound (another reviewer already commented on being able to climb walls), and that the art and music/sound is as nice as you can manage. If you do feel ambitious enough to make the gameplay itself challenging or add crazy new mechanics like a ricocheting clone teleportation mechanism or smth then go for it, but it doesn't seem like that sort of stuff would be necessary if you've got a great story to tell.
Of course if you're doing one game a week for a while, then a big extension of this idea might have to be put on hold or take the back burner as a side project for the time being.