Literally no it is NOT. Being a cuckold involves a level of denial and humiliation. Watching your love interest fuck someone else and either enjoying it or being ambivalent is NOT cuckoldry. Swingers are a thing. Open relationships are a thing. Not being a possessive tool is also a thing. None of which necessitates cuckoldry.
If you think the scenario you listed is de facto cuckoldry no matter what, that says a hell of a lot more about you than it does actual cucks.
You are mistaken in the premise of your argument because you mistook the meaning of what
TheSmoothCriminal said.
There are two words that you used that have different meaning, yet you used them as if they mean the same.
Cuckold - Evolutionary biology term referring to a male/husband of a cheating female/wife. Here there is no involvement from the husband, and in this scenario, there can be denial and humiliation as you stated.
Cuckoldry - This is the kink named after the evolutionary term and here the husband is actively involved because he gets sexual satisfaction watching his wife "cheat". Ther can also be a humiliation aspect, but it is staged/faked for the benefit of the husband's kink.
In its archaic meaning it was exclusively used to define the action of cuckolding or being cuckolded, but it is now seldom used for that purpose.
Now the term cuck is used to describe the man involved in either one of those indistinctly. When he referred to someone being the definition of a cuck, we all know he is talking about the reader and not the MC. Your argument of being in denial works for the MC but not for the reader. The tags in this site exist for the benefit of the reader not the MC. He is correct in calling a reader a cuck in that circumstance because he is referring to the kink not the biology term.
Before you start thrashing at your keyboard, remember that in literature, a whole system of classification exists for works based on content (drama, science fiction, comedy, etc.). This is because it is recognized that this works elicit feelings in the reader and each reader has a preference.