I think I get what you are saying, but not sure. What is liberalism, BTW? Liberalism used to refer to philosophy of English enlightenment thinkers like John Locke and had natural rights as a large part of it's foundation. Today? well... hmmm... What is the intellectual foundation of today's "liberals"?
Not ceding classic liberalism with the word is the point. (Because ceding too much of it puts you at danger of a populist takeover, i.e., "literally Hitler".)
Skimmed the beginning, will read the rest later. Liberalism is definitely modern (it's from the enlightenment), it's definitely British (ie. has nothing to do with Rousseau)... I'll have to read more to see why the author thinks it's not political.
I personally like that they are embracing "progressive" more. I think it's more accurate than "liberal" and uniquely theirs.