This looks like market segmentation and not misogyny. If the known market for Borderlands is mostly male and some large percentage of those males have a girlfriend, it only makes sense to try to attract that segment to the product.

Actually it seems quite the opposite of sexism since they're deliberately trying to make the game more accessible to women.

Note this does not mean women are worse at first person shooters, it just means that the game is currently designed for "experts" and there's an adjacent segment that gets exposure to the game via watching their partner play. "Girlfriend mode" is an attempt to reach that segment.

Having a "boyfriend zone" in a women's clothing store would be analogous and also not sexist.