The first space liquor probably won't be whiskey. Whiskey comes from corn, and corn needs some space. Rice-based liquor is more likely, since rice needs less space. Or most likely, it'll come from whatever plant material the astronauts happen to have lying around. Nobody said it was going to be good liquor.
Fermentation will be a little tricky, but not spectacularly so. Yeast doesn't care about gravity, but a basic centrifuge would be necessary to ensure the yeast gets everywhere throughout the mixture.
The big problem is distillation. Back on Earth, you distill with fire, and there is steam, and chemicals are released. These are things you don't really want on a spaceship. However, you don't actually have to distill liquor, according to the article. There are other, safer ways of doing distillation's job using pressure differentials. And wouldn't you know it, there's a whole vacuum outside the ship! How convenient.
I don't know about you, but I'd drink space booze. I'd drink space beer too. It wouldn't matter how bad it is, and I'm assuming it will be pretty bad. It's space booze. You gotta drink it.