The short answer is that yes, it's legal. The long answer is that technically it's not legal, but due to how prohibitively expensive it is to pursue, those that are entitled to do so, don't bother.
If you charged to play a particular game (which we don't), then the studio that created that game (or their publisher) could go after you for damages (which would be difficult to prove). The damages would be a negligible amount though, especially compared to the time, energy and money that resolving that court case would require.
And that is why places like Howie's Game Shack can exist, and why people can hold public tournaments for all types of games they don't have commercial licenses for (because commercial licenses don't exist for most games).
However, we avoid the entire situation anyways by just charging a base cover ($10 a day) for the entire gaming area (no quarters, no hourly rates). You aren't being charged to play any games, you're just being charged to enter the area.