I think you are not understanding his characterization of "right" - he is not referring to right as a political right, he's using it as a replacement for "the good side, the correct, the moral".

He mocks the notion that someone could deal in absolutes. Because he's a theist, he even goes as far as to say that Absolute good can only be defined by a God. So, he mocks the lack of humility from someone who is grandstanding by using the phrase.

A few years later, he writes a book about the phrase, as I said, and that he knows the correct and moral things. He is trying to fight history revisionists (which I agree that we ought to do so) but declares himself to be on the "right side of history" (again meaning the correct one).

As far as me reading the book, I've read excerpts, so I know the content of it, at least in a general sense. However, my point here is not nullified by some nuance you can find on chapter 3 or something of the sort.

Simplified.-

1. Grandstanding is stupid, Judgement is for God alone.

2. Look I wrote a book judging everyone who got it wrong.

3. Foot in the mouth.

He may very well be 100% accurate on his book mind you, my critique is not of the content of the book itself. If you want to harp on that, don't bother. My critique is on what I've tried to simplify in two points.