You'd probably have greater success challenging the "XKCD guy's" assumptions if you adopted a less belligerent tone. I don't know nearly enough to verify who's right here, but some things that strike me as questionable:

The most fuel is spent relatively low in the atmosphere.

This is consistent with most fuel going into producing kinetic energy.

1 - accelerate to the Moon - from 8 to 10 km/s

Generate a delta-v a fraction of the one you needed to reach orbit, in vacuum, with an engine with a higher specific impulse than that of the Saturn V's first stage, for a small fraction of the launch mass. Yep, shouldn't take that big of a rocket.

2 - decelerate to Moon orbit - from 10 to 2 km/s

It is seriously more complicated than that. Same for returning to Earth orbit.