It was not for their personal interest _they did that.

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.

it 做形式主语，it就是后面的they did that
it做形式主语的时候，在真正主语前要加that

强调句固定句型。

看句式变化。

1. I like the food. -> It's the food that i like 强调宾语。

2. I like the food because it's delicious. ->It's because the food is delicious that i like it.强调原因状语

3.I like bananas. ->It's me who（that） like bananas! 强调主语。

强调句是固定句式,it's...that(who)...

当强调人的时候看可以用that和who强调的是其他方面的时候只能用that.

你这个句子也是强调原因，只不过是否定而已。