It is ( )Tom often surfs the Internet playing games ( ) make

应该选C.
题目的两个空分别考查的是名词性从句和强调句的用法.
第一个空是主语从句.也就是考查that连接陈述的名词性从句.连接词that本身没有意义,不作句子成分,只表示从句的开始,位于句首时,that不能省略.题目中that连接“Tom often surfs the Internet playing games”从句,充当主句的主语.又是位于句首,固不可省略.
第二个空考强调句.句型结构是“It is/was +强调部分+that（who）+句子的剩余部分”.此句型可以强调主语、宾语、表语、状语.在这个句型中It is/was和that（who）没有实际的意义,只是用作强调的结构.所以当我们把It is/was和that（who）去掉后句子应该还是完整的.
回到题目中,题目里强调的就是由that连接的主语从句that Tom often surfs the Internet playing games.那么把这个句子还原就是：“That Tom often surfs the Internet playing games makes his parents very angry.” 句中的"That"不可省略.
原题句意：正是Tom经常上网玩游戏 ,使得他的父母很生气.

C. that; that
前面THAT是同位语从句. 后面THAT 是强调式的THAT,
等于下句定语从句.
Tom often surfs the Internet playing games , which makes his parents very angry

B
首先选择第二个空强调句型去掉it is ........ that 后仍然成立，我们就去掉。
这个是由what引导的主语从句！
如果不擅长语法，就排除

D

选A强调句型

选B。

C
It is......that是强调进行,将此结构拿开，句子依然成立