The crucial difference is that gaming is, at least theoretically, discouraging the user from it from an economical perspective, whereas for Bitcoin the more power you consume, the more positive your balance will get.

No matter how polluting, running around with a sports car will in some way counter most users' personal finance. But if using cars made free money, not only nearly everybody would be doing it, but there would be potentially no limit to "scaling up" the earnings, as long as one could cover the initial investment.