He drinks because he really needs a drink at this point but also because he has to stop him from saying something really stupid. It's like he's in a fog, the situation feels unreal, it's too bizarre and horrific. Standing in this Arcade Wonderland, so bright and shiny, while Quill tells him about killing entire civilizations.

Ezekiel coughs a little and is almost tempted to ask for something stronger than beer.

"Only in video games."