Although in English there aren't quite as many compound words to capture the meaning like "the activity of pouring water into gopher tunnels in order to extract the gophers", the phrase 'gopher flooding' can be used as the closest and most concise substitute. Nem túl meglepő módon az angol szó, "flood", lehet tárgyas vagy tárgyatlan ige. In any case, this is the most accurate and neutral translation I can think of, considering the articles on the web.

Since it sounds like you are looking for terminology with respect to a game you may also consider "Gopher Wash Out" as a title (if that's what you are looking for), as this sounds a bit more playful.