By the right do you mean the true Scotsmen?
He actually referred to both of them as "the right", so why would you think he is excluding some from actually being of the right? I see no place where he employed a fallacy.
I think I know what you are alluding to, folks that draw lines in the sand and claim "X" isn't a true person of the right. The American right is composed of a very diverse spectrum of people. It is not a progressive revolutionary movement united behind changing or destroying our institutions and culture like the left. The left is an accurate descriptor, when in power they move policies to the left. The "right" very rarely when in power moves things to the right in any lasting fashion.
Right
in
name
only
The right is an incoherent group that is reactionary to change for the sake of change. There is no overriding tie that binds the right together other than an ill defined commitment to the constitution. Being on the right practically means nothing more than "not a Democrat".
In fact, there are many leftists active in the American right political sphere. That is why I consider the American right to be incoherent. If a person identifies as part of and is active within the political right sphere, yet holds presuppositions, political philosophies and even policy positions that align better with the leftists, are they still of the right? Is it a fallacy to question whether the Neocon never Trumpers are actually men and women of the right? Or is "the right" a content less phrase that means whatever the current zeitgeist calls the right?
I'll still use the word "right" as a placeholder much as perd did, but I do it with the realization that it is a broad, ill defined word that at best can be defined as what it isn't relatively, ie a Democrat.
The subversion of language continues unabated.