What is game studies?
Game studies is the academic study of games. That may sound like a circular answer, but it's perhaps the only agreed-upon definition of this diverse and multidisciplinary field. Game studies doesn't belong to any particular department in the academy, and exists across the arts, humanities, and STEM. Many of my favourite game scholars work in Cultural Studies, Theatre, Communication, and English.
Game studies is very different from game theory. The latter is a series of thought experiments in neoclassical economics, demonstrating how rational actors behave under competitive circumstances. The claims of game theory are virtually impossible to test, and the real-world existence of rational actors is questionable. Either way, it exists far outside my field of interest.