Definitely South Dakota stretching in the background, not sure who's playing Go with Taihou, could be Tirpitz or Enterprise or Belfast or Washington...

i think it might be seattle.

Taihou's Go partner's hair is too short to be Enterprise or Belfast, and I don't think Tirpitz or Washington would need to tie up part of their hair with how short theirs' is. I think Seattle has part of her hair tied up like that in her in-game appearance...

More importantly, why does Hiryuu look like she's resisting the urge to pounce on Sirius?

That's a very flat looking South Dakota