No, playing arcade games is not gambling. She's not talking about Space Invaders. She's talking about the games where you put a token in for the chance to win more tokens. That's what gambling machines are.
It sounds like she may be trying to teach you some responsibility. Get yourself a part-time job and start saving your money. Then maybe she will help you pay for a good car. Even if she doesn't you're going to need to do that anyway.