Having looked into it a little bit, I realized that my game doesn't use Java. I made it in Construct 2, and it does in fact run in HTML 5. I've since taken down the "requires Java" icon, though, thank you. Oh, and thank you for judging the game on its own merits, I appreciate that.
Which mode were you playing? Sounds like the "Race the clock" mode? Did you fill all the squares, just connecting the gems is only the first part of it.
There are a couple control schemes that you can try out in the options section of the main menu, a couple of which use arrow keys for movement. Those might cater better to left-handed players.
The update made it so that you can't get stuck on a level with no money to upgrade, but on later levels you now have a lot of money but no more interesting guns to buy. The levels also stop being challenging at that point, and all you have to do is point a gun in the general direction of the enemy. Perhaps a sequel could address those issues?
Works fine over here (Ubuntu 13.04, Firefox 23) - what platform are you on?