I'm on a laptop running Ubuntu MATE. It's admittedly pretty old (circa 2011), but other Unity browser games run fine. I get the same problem on both Firefox and Chromium (also regardless of whether or not it's fullscreen - the display is 1366x768).
If other people have been able to play it then I wouldn't worry too much - I mostly mentioned it in case it was one of those problems that creeps in the moment you export a game. The first HTML5 thing I put together wouldn't even run for reasons that weren't at all apparent when I previewed it in the editor.