游戏厅 is a place where people go to play video games, often in the form of an arcade or a gaming center. It's a compound noun: 游戏 (game) + 厅 (hall/room). In mainland China, these are usually commercial establishments with coin-operated machines, though the term can also refer to internet cafés with gaming areas. Be careful not to confuse it with 游戏室 (a smaller game room) or 网吧 (internet café).