把句子这样调正一下,兴许你能明白.
That they did that was not for their personal interest.他们那么样做并不是为了他们的私人利益.
That they did that 是主语从句,也就是说原句中it不是真正的主语.
举个例子：
That I love you is known by everyone.大家都知道我爱你.
That I love you 主语从句
也等于：It is known by everyone that I love you.