Continuity mistake: When Martin is at the Hippo Club and goes to the bathroom, he washes his hands and throws the paper on the floor. You see the paper on the floor as he leaves in a wide shot. In the last part of the scene there is another wide shot and the paper is gone.
Plot hole: It makes no sense that Martin would be getting the invitation to the reunion mailed to his office (or to anywhere else.) He's had zero contact with the alumni committee, and they're not going to hire a private detective to find him. He also doesn't have contact with anyone else from his hometown who might have forwarded it; his father's dead, and his mother's not in her right mind. There's no explanation for why it would have ended up there except for needing to set the plot in motion.
Factual error: In the scene at the Cuppa Joe, it's a span of 3 minutes and 5 seconds from when the server takes their order to when she's walking back to the table with the food - that's not enough time for an order of pancakes to even finish cooking, let alone for all of those ingredients to be cooked and plated.
Answer: No, Doom II was never available in a commerical arcade cabinet. It must have been specifically designed for the movie.
Ral0618