Wait, "game criticism?" According to the MFA program's website, students can focus on criticism for the game design degree, "which means writing about games with a focus on game design and player experience." The site further adds, "A student with this focus will be well-prepared to become a game journalist or critic, a theorist or researcher, or a scholar or historian." There is no mention, however, of the crushing debt you'll be unable to pay with a game journalist's salary. We kid!
Regardless, between creating individual projects and working in groups, the NYU MFA program intends on educating future game devs in a wide variety of disciplines, across a varied spectrum of virtual platforms (from social to console, and everything in between) -- even game journalism, it would seem. Interested parties can find out more info through NYU's graduate program portal, but you'll probably want to read this FAQ first. That thesis sounds like a doozy!