Perhaps he was a nazir who just finished bringing his korbanos and now was drinking wine. If he was a kohen I hope he wasn’t drunk during bircas kohanim.
One should not poke fun c”v at the Torah. Every letter, tag has innumerable lessons, derushim, remazim etc. In fact there’s an important lesson why the Torah goes here at great lengths to specify each, seemingly identical, Nasi’s offering.