That's the point though. The "serious plot" is a parody of their usual serious plots, they ramped up the corniness on almost everything. Buffy and Angel's heated talk, Giles trying to talk to the spirit world to see the future "because he has to try". The end discussion where they are talking about it at the picnic bench. "I'll never forget it's face... it's true face, I mean." "Buffy: 'That was the bravest thing I've ever seen.' 'Giles: The stupidest >_>'".
Plus the giant actual battle that it only cuts to briefly. "Oh my god, it's grown." And all the hectic scenes of fighting.
Everything the gang says when it cuts to them or when Xander runs into one of them basically amounts to "oh my god end of days it's the apocalypse the worst we've ever faced." But that's the joke. That's what they are always like. Like, when Xander runs into Angel at the Bronze, and Angel is like "Thing's are bad, they don't know what they are dealing with." That's a parody of how Angel always knows when something bad is happening and comes to warn the gang, and he is EXTRA CONCERNED now.
The point of the episode is that's a reversal of the usual formula of an episode. Normally an episode of Buffy and most shows like it has an A Plot about some bad guy with some action and a B Plot involving development of a character. This episode is supposed to turn that convention around and make the development of a side character the A Plot with a world ending disaster as the B Plot. You said you would have preferred it more if it was primarily about the gang fighting a group of demons with Xander having a side adventure, but that's exactly the opposite of what this episode wanted to do.
I thought they pulled it off beautifully. The Zeppo is honestly one of the best episodes in the series.
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The batman villians all seem to be one big joke that batman refuses to laugh at - SantaRPG