I also have an instant-run port of Cave Story: https://thelongestyard.link/cave-story/. For that one I added cloud save game sync too. Porting classic games to the web is a fun hobby!
Coming up with touchscreen control schemes for these old games is probably the most interesting part. I really like the controls I came up with for both games. For Quake I determined that you really need automatic shooting for touch controls to feel good, but a naive implementation of an automatic trigger makes the railgun into a win button, so I did something a little more complex that I think is fun to use and not unfair. Cave Story was also challenging; at first I wasn't sure I could make a touch control scheme that would be good enough to beat the game, but with the final scheme I was able to play all the way through (at least to the first ending) purely on touch controls. And you can use the cloud save sync to transfer your save game to a PC for the hard parts if you need to.