Hmm... that is strange. You might find more luck trying out the standalone version, since WebGL can sometimes introduce weird artifacts like this in browser builds. I'll look in to seeing if this is something I can fix in the 1.7 update!
I am having a similar issue and might be able to provide some more information:
I am running the game through wine (as I don't have windows) and the controls work fine (both minesweeper and tetris). That is, until I interact with some other window (e.g. alt+tabing to discord) From there on keyboard inputs no longer work.
I tried having wine emulate a virtual desktop in order to have the game as a window, rather than in full screen. There keyboard inputs do not work right away. My guess would be that there is some issue with losing focus.
One way to solve this (at least for me) would be to have a download for the web version, so one can run it locally in the browser, without an internet connection.