It's a good thing Marten lives in a comic strip. If he were a real-life dude, downing an entire bottle of hard liquor by himself goes past "This is an unhealthy way of dealing with your problems" to "Seriously, you might die." Also, being punched hard enough to lose consciousness is a great way to get brain damage. Luckily for him, he does live in a comic strip, so all of that is nothing more than humorous exaggeration.
Or, given the context, not humorous per se, but for the dr4maz.
Anyway, it seems to me that this indicates that while Dora has issues with her anxieties and insecurities, the particular insecurity re: Marten's feelings for Faye was not completely unfounded. Which, really, I think they all knew: he spent months of QC-time wanting her, and you don't just turn that off like a faucet. But then warning blatant gender-based stereotyping approaching guys in general are often known to lust after most any attractive person-of-an-attracting-gender they know, and most guys manage to remain faithful to their partners anyway; so Marten was presumably sincere in his protestations of being committed to Dora. That doesn't mean that he doesn't still have feelings for Faye -- as shown here, unfortunately in the form of drunken come-ons.
Anyway, in this particular case, Marten is being an asshole, with only the tenuous excuse of being miserable and drunk, and Faye is being violent, but by the standards of the QC-verse not out of proportion to the offense. My guess is that in the morning they'll forgive each other the particular offenses, and the main fallout from this will be, "What did Marten's drunken confession indicate about what he's really feeling?"