Wow, really nice idea. The sound is loud and jarring, and should at least have a mute option, but the graphics style didn't bother me. In fact, the line-style really fits the dimension hopping motif. From a geometric perspective, this was pretty cool. I had trouble actually envisioning what each new screen was going to look like, but you've made the path through every level pretty clear. Once we start having multiple options, it will get difficult. I envision a lot of running in circles.
Make sure you have a "return to title" menu at the end of your game. Otherwise, the game just sits there on "to be continued..." and the player has to reload the entire page if they want to play again.