In theory, you would need a degree/diploma/whatever in anything similar to programming (computer or web) or other gaming-related studies (like 3D modeling/animating).
In reality? They don't really care; as long as you're over 18 years old (because of laws related to work with things potentially adult-rated,) you finished high school, love video games and have a keen eye to spot bugs, you're good to join in! XD
It is however a good thing of having higher education (although they don't mind exactly in what, there's a bunch of coworkers of mine that studied in arts, linguistics, secretary...) and even better if you're fluent in speaking in another language other than English, especially if said non-English language is your native one ^^ Puts more chances on your side