这句话应该是It was yesterday that he played.
It is/was.that（who）.这是一个强调句式.
比如：
It was Mary that saved me.正是Mary救了我.这里就不需要用who了.
It was Beijing that I love most.我最爱的地方是北京.这里也不需要用where.
强调句式是主导的,要服从它的规律.
附加例句：
It was on Monday night that all this happened．所有这一切发生在周一晚上.
It's me that he blamed．他怪的是我.