The joke is that this ancient demon who had existed for thousands of years was reduced to a verbal slinging match of immensely juvenile proportions. It's a scene that's knowingly immature in a comedic sense. Whether you thought it was amusing or not is another matter, but I don't peg it as being badly written.
I thought DmC was a consistently funny game that had the good sense to (rarely) ever take itself too seriously. There are heaps upon heaps of games out there that have the dreaded combination of being both terribly written and po-faced, and anyone who can tolerate a dark soul filled with light should have little trouble sitting through DmC's cut-scenes.
Yep. I think a large part of negativity towards the scene, beyond simple disdain for the reboot on a conceptual level, is a knee-jerk contempt for profanity that some people have. Start dropping f-bombs, and accusations of poor writing aren't far behind. I remember people getting similarly bent out of shape about the language in San Andreas.