Wow, this is really well written! The back and forth between the two of them is really well done and fun to read.
I liked the setting too: the lift being blocked when Kaiba is around not just being a coincidence made it all more plausible, and the few times physical closeness comes into play, it's never overdone.
I loved how you portrayed Mokuba and Jounouchi as well.
I'm a little confused by Mai's story about why she wasn't duelling anymore; I'm thinking that after the duel against Yami Malik and the horrible results of her losing, she couldn't manage to try not to win anymore, but I don't think she says anything like that, so I don't know if I'm completely off or if it's not supposed to be more clear, or if I've missed an important point... cough Sorry if so.
Also, I don't know if that's just me, but some of your paragraphs are a bit long, which can be tiring when you're reading from a screen.
And they played speed! I was almost addicted to that game for a while, and it's fun to imagine them playing it; especially since I'm sure they'd both be really good at it. :)