The phrase "to buy the game" means to purchase or acquire something, often a product or service. In this context, it refers to purchasing a video game for one's personal use or enjoyment.
Sentences with «to buy the game»
If you don't buy this game for graphics you are and idiot. (metacritic.com)
If you plan on buying the game on PC, don't buy it. (mmogames.com)
If buying a game for a kid, make sure you have a number of choices. (hardcoregames.net)