An excellent framework for character analysis, and I agree with every one of your takes. The way you described them, I could see them in my head pulling all their moves in-character.
I also agree with Phantom that J'onn could turn out to be a great player. I imagine he might lose on purpose anyways when the game starts to heat up.
Constantine is obvious, but I can see him getting burnt out and losing his edge in the later stages.
Catwoman could be good, but I think she cheats.
I don't see Arthur playing as well as the best of them; he can make some basic strategic plays but he might be too transparent in his bluffs.
I think Shayera is sharp enough to do well, and Carter has a decent poker face but isn't patient enough to play for too long.
It's fun to imagine which players trump other players. Bruce is so calculating that he probably hates playing with Hal, since he's so erratic. Or does he find him easy to manipulate as a result? As was said in the OP, John might be even more formidable as he's more methodical in his boldness. As you mentioned, Dinah plays Ollie every time.
Oh, I've only just noticed I commented on this thread already. Well it was a nice re-read.
1. Like Dick, all Robins would be very good at playing. However, Jason would be a bad loser and a great winner. Tim is great at reading people, but he would grow too paranoid as the night goes on, and either ends up losing everything, or just drinks enough coffee to keep playing until the perfect win. Damian would lose to Alfred every damn time.
2. I'd pay to see a poker showdown between Lois and Selina.
3. I wonder if Arthur and Mera allow casinos in their kingom. Mera would probably be very good. Arthur, maybe not that much.
New 52 Dick can read micro changes in expressions and body language. I don't know if they will keep it, but he did win a card game because of it
Never try to bluff against Lori Lemaris.
John Constantine pretty much sums it up, he hasn't hesitated in uping the stakes by putting his soul in the pot.
Outside of that, I imagine Zatanna would be pretty good with the cards, Batman if he has the inclination to play, and Hal Jordan...I imagine having no fear makes you a pretty good bluffer.