would you mind his playing the computer game in your room?

mind one's doing 介意做某事
这里牵扯到动名词复合结构的用法：
动名词的复合结构
即“逻辑主语 + 动名词”结构.动名词的逻辑主语由物主代词或名词所有格充当.如 David’s opening the window made us angry. / His coming late has some reasons.
注：当动名词本身在句中作宾语时,在口语中,逻辑主语还可由宾格代词或名词的普通格充当. 如 I enjoy your/you playing the piano.
希望我的回答能够帮到你.祝你学习快乐.O(∩_∩)O
这句话的意思就是“你介意他在你房里玩电脑么?”毫无争议!
再问： 我书上给的答案是 你介意我在你房里玩电脑么 。。。我去。。。