"Recharge a game" can be referred to as "top up a game" in Engpsh.
This phrasing comes from the practice of topping up a mobile phone or other similar devices with credit or money, which can then be used to purchase various services or items. In this case, the service being purchased is the abipty to play a game, or to buy virtual items within the game.
Example sentences in Engpsh and their Chinese translations:
Can I top up my game account using my credit card? (我可以用信用卡充值游戏账户吗？)
I need to top up my game account before I can buy new skins. (我需要充值游戏账户才能购买新的皮肤。)
I've just topped up my game account and now I have enough coins to purchase new characters. (我刚刚充值了游戏账户，现在我有足够的金币购买新的角色了。)