I'm having issues playing the game. I got to the first level, pushed the arrow keys and WASD keys several times and finally got the guy to run full speed into the first obstacle, without me controlling it.
Clicking on the game or anywhere else doesn't seem to have any effect at all. Sometimes you need to "lock" the mouse onto the game by clicking in order for it to work. This does not seem to be the case.
It looks pretty great for a test project as you say. It may or may not be in your control to fix this problem. Normally Unity works very well on my computer, but semi-rarely it behaves strangely like this. I don't think it's a problem on Unity's end but perhaps something with the game itself.
I'm on a Mac running 10.11.2 (OS X El Capitan) and Safari 9.0.2 which are currently both fully upgraded.