Probably not, at least for now.
I don't really know how to make a browser version, and I don't have enough free time to learn how to do it properly at the moment. (I spent it all to create downloadable version)
Also, one of the main things I wanted Height Shift to have is the ability to bring your own characters and customize the game with your own files, which would be much harder to make work nicely in a browser.
So I definitely wouldn't expect a browser version in the next few months, and honestly I'm not sure if I'll ever make one. For now I'm sticking with the downloadable version :)