Does he usually seem drunk when he's explaining things?
I wouldn't characterize the way he was acting as seeming drunk. Rather, he seemed animated, probably because this is stuff he so deeply cares about.
From what I recall, Feynman was an excellent explainer of the abstruse concepts (I.e. Feynman diagrams). And I think most physicists strive to make that simple explanation. Here, Feynman talks more conversationally rather than bogging down the questioner in incoherent jargon.
As a side note, I believe he was teased by other physicists (notable ones) for his New York accent.