Practically speaking, it's a service job, but it's a tricky one. Let's say you've got five players on average, and a game session lasts four hours. Your hourly rate ought to be at least $15 an hour, so you're looking for $60, or $12 from each of them.
OK. How does that compare to how much people currently pay to game? A convention slot will run somewhere between free and maybe $8 per slot, the latter being for something like Gencon. Gaming stores that charge for space don't usually go above $5 an hour, I don't think. So you're already needing to charge somewhat more than what people usually pay for a game. This makes it a hard sell.
Also, you're not really making $15 an hour there, cause you've got to pay for prep time plus supplies.
And then you've got to fill 40 hours a week with game sessions in order to make it compare to a fulltime job.
People do try this from time to time; there was a guy on ENWorld and RPG.Net, Captain Commando, who badly wanted to make it work. I don't think it did, although that might have been due to his marketing as much as anything. I've also heard of people selling GMing as as a children's party service, which makes sense -- parents pay for clowns, so if you market it as an educational activity, that might work out.
Still and all, freelancing is a better way to make a living out of gaming, although that's a different set of skills.