"To download the game" means to transfer and save the game files from the internet onto your device so that you can play it offline or whenever you want. Full definition
You can start right now by downloading the game for free! (propcgame.com)
Whichever games you decide on, be confident to only download your games from very good, reliable sources. (mindfullyfrugalmom.com)
Despite its rumored gradual decrease in popularity, Call of Duty: Black Ops III remains at the top of the most downloaded games on the PS4. (gamingtrend.com)