Short answer: not necessarily. Threads likely have nothing to do with it. In fact, depending on the number of threads the machines can run, the overhead to spin one up, and the actual parallel work you do, you may wind up performing worse.
Performance is subject not just to the quality of code, but to the quality of the machine running it. So, it stands to reason that I'd expect a faster machine geared to gaming to perform better with a game than a school computer using lesser hardware.
That's not to say that your code couldn't use a refactoring, but in general, a machine that is better performing will be able to handle things better than one that...isn't.