I can't recommend CleanMyMac, or MacKeeper, or any of that sort of stuff. Usually causes more problems than it fixes. What you really need to do is get an external HD (or at least a USB thumb drive) and move off any of the excess stuff (usually videos) that are taking up too much space on the boot drive. Even if stuff like CleanMyMac actually worked, the savings would be minimal and a month or two later you'd be in the same mess. Throw out stuff you don't use or need or have watched, park the media files on another drive as much as possible if you're running low on space. Believe me it makes a real difference to how well the Mac performs when you have 20GB or more free space.
Ah, a boarding school guy! Heh, I was one of those a million years ago ... when the Earth was still cooling ...
Anyway, IIRC Kongregate uses Flash, so that seems to be the problem. I haven't been on that site for a while but I used to enjoy Monsters' Den and Book of Dread a lot. Just checking it now I'm getting a Flash error message, I'll check my settings and report back.