Okay so it's not the punchline of the scene, it's just something wacky that she's arbitrarily doing "because drunk". Had she skateboarded over with a pangolin under one arm, I'd have been no more entertained.
So.... Walk over and sit down next to him? Maybe I'm just a kill-joy, or I'm too old to think of drunk people being dumbasses as a for of humour, I can't offer a better explanation for my disinterest in this scene.And I wouldn't say "quirky", I'd say "very drunk, and talking to someone ankle-high".
Eh, I wouldn't call it weird, as such. It's the same as watching your brother approach a girl in a bar and act awkwardly; doesn't matter that it's your brother, but the situation can still be funny and endearing.
Like John Cribati said; she's shipping the unintended bromance, not cat-calling for them to bang right there on the spot.