The game site does not need to know what your capabilities are. If you try to run it, and it doesn't work, you don't try again. It doesn't need to know *any* of the fonts or even font-families you have installed, it just needs to do what the web has always done; Present a list of fonts the site designer would like the browser to use, if they are available and the user allows it. No site needs to know even the simple small/med/large screen size, as that can all be (and usually is) handled entirely within the browser via CSS.
Give them even less info than you propose and it'll still be too much, generally speaking.