Good Q. It's definitely not gambling. There's no chance mechanics....just pure skill-based play.
Those that are good at the games get rewarded based on how skillful they are. Those that aren't, simply have fun like on a typical P2P arcade cabinet.
Would there be a bet limit? Because if someone gets really good at the game, they can just bet a ton of money and make a dent in the arcades bank account. Also, it's worth noting that most arcades use a card system where you put some money on a card and spend it, so having to log into an account. It does seem like an interesting idea, though.