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However, I can't predict if G will be OK with your flash arcade site. G is very alert on copyright issues (concerning flash games and stuff).
My guess is that Google would say it's not allowed, especially if there's any cross-linking and shared traffic between the sites. Gambling sites are getting a lot of heat these days.
P.S. It should go without saying that we can't speak for Google on this matter. You should ask them if you think there's any question.
Site may not include
Sorry, Jomaxx is right about this.
I was a bit confused because the Adsense T&C state
You shall not (...) display any Ad (...)
on any Web page or any Web site that contains any pornographic, hate-related, violent, or illegal content (...)
I don't understand wy both "Web page" and "Web site" are mentioned. I also think it is strange they don't mention the gambling part here.
However, Jomaxx is right, no gambling on your "site". But the question Jomaxx raises is also very interesting: what is considered a "site"?