This is kinda cool. The only things I would say to be tweaked are that 1) the keys still affect browser scrolling -- specifically, when I hit up and attack to throw a star or down to change menu options, that makes the browser window scroll. 2) When I played the game once and then said not to make me do the tutorial again it made me do the tutorial again. 3) After I died the second time I said I don't want to continue and was put directly back into combat on level 1 (without the tutorial). But that seems kinda random because I tried it again after dying a third time and it behaved as expected. Using Chrome on Windows. Less critical: some people like using up arrow / W to jump so maybe make those keys do that (with some other way of throwing stars), and if I click the webpage outside the game so I can't control the guy any more I'd like the game to pause until it regains focus. Overall I'd say this is a good start at making a great platformer along the lines of Ripple Dot Zero or Phoenotopia if you're feeling ambitious enough. 4/5 only because it's still just a demo.
Edit: FWIW I wrote that while the game was still under judgement and I couldn't see the other reviews. Guess it's nice to see that I'm not alone.