In some respect Europe is ahead of us because they have genuine longstanding political parties on the right. We don't, and our political efforts go mostly into fighting the GOP rather that making real change. But I agree that in America one finds clearer conservative ideology. On the other hand there are no monarchists to speak of in America, and that is quintessential right wing.
ascendency of the individual over the state (rightism)
That is not "rightism", that is libertarianism. Indeed, that is less in evidence in Europe, but let us not switch definitions. The Right wing implies, for example, nationalism, and the libertarians are barely waking up to the issues such as national borders, and are uncomfortable with nations becoming a part of the political language.
Your claim that the American understanding of “rightism” isn’t the true understanding just points out your fundamental lack of realization that we’re talking about two different political axes here. The term “right” isn’t used in the US in the way that you seem to believe it is. Trying to conflate the European “right” with the American “right” is nonsensical.