I think that at about 1:20 he's chastising those who disagree with him as being "demagogic politicians" (soft g), i.e. those who indulge in demagoggery (yeah, I know, I just want to spell it like that).
In other words, he's not saying 'demagouge,' which I assume is the point of this post.
David Beamer, did you mean the spelling in your title as it now stands (demagouge)? Or are you rather, as seems appropriate, interested in the verbing of demagogue?
Yes, I did mean it: TPM oddly identified "demagouging" as their word of the day instead of "demagoguing", itself long attested. But after all, and as I'm sure you'd agree, Mr. Jiff, people make mistakes.
— David Beaver
Well, 'rouge' is a word in its own right, distinct in both pronunciation and meaning from 'rogue'. (There is a book called Going Rouge. It is not the same book as Going Rogue.) So if it becomes an accepted spelling of 'rogue' that may cause some confusion.
"[...]their name stems from the red or pink makeup they use to add colour to their cheeks. In contrast, rogue administrators wear only aftershave. And clothing.  Once in a while. "
Chaise lounge originated as an eggcorn (or perhaps just misspelling) and is surely typically still used that way, but the term has been coopted (at least in Australia) to refer to a piece of furniture which is a cross between a chaise longue and a sofa. For example: http://store.unitedhouse.com.au/store/lounge-suite-6.html