I was having a similar problem with another game, and I had a similar desire to learn general troubleshooting rather than have someone give me a specific fix. That said, I don't know if I can help because for me it's basically butt my head against a wall until I poke something enough that it works - usually I don't know enough to understand why the thing works.

I was installing my games onto a secondary drive. The problem turned out to be that that drive had been formatted by Windows back when my computer was set up to dual-boot. Some games still ran fine in Linux, but this particular game nothing would happen when I clicked Play. On a whim I tried installing it on the primary drive with the OS, and it worked first time. So there was something about that game that didn't work with the drive formatting.

(I've since reformatted the second hard drive so that everything should now play nice with Linux, now that I no longer have Windows. Game is fine now.)