My game room is clearly the exception, we have a 'frieze' which is basically a low shag. Very soft and easy on the feet (we require guess to have their shoes off) and also keeps the sound rich without echo and gives the room some warmth vs hardwood or industrial carpet. It is a good quality and once a pin is moved, the indent from the legs does disappear after a short amount of time. The big drawback is moving the machines is a little bit of a pain, but the reality is I don't move them often. It is easy enough to move a machine when you need to get between them. Part of the reason for the choice was that my daughter was a toddler at the time, so we wanted something that would be friendly for sitting and playing on the floor, which even though she is now a teenager, is still nice when families come over.

We have had a similar setup for over 10 years, the carpet (a frieze) still looks great (we do not allow shoes). We have a few parties each year without incident (almost all of the machines have a pin gulp). we have just a single stain that is barely noticeable (and that was when my daughter had a party and someone spilled orange crush and did not tell us). Moving machines is harder then on hardwood, but we don't move them too often and it is not that hard to do it (turning the lift cart with a machine on it a little tricky). After moving machines, the indent caused by the legs disappears after a couple of days.

I've seen some folks go with a hard surface and then put carpet strips in front of the games, that can easily be removed to move machines. Standing on a hard surface for long times can be tough on the body/back.

No flooring solution is going to be perfect, so you need to decide which attributes of a game room are most important to you. Ease of moving machines, comfort while playing, noise/echo reduction, cost, maintenance/clean-up, etc. Once you are clear on those things, will be easier to decide.