You kind of cherry-picked two paragraphs and butchered the article. The article's point is that Reconquista, with capital R, is not a good designation for the historical events that took place. It does use the term throughout the article, though, which maybe is a bit confusing. But if you read a couple paragraphs past the one you quoted, you'll see it restated that the term Reconquista is a 20th century invention. "The idea of Reconquista" is talking about the idea, specifically, not the term; the term, and mysticism surrounding it (like the originating battle that actually never took place as such), part of which is debunked also in the article, is modern propaganda.
You're ignoring what I actually said about the quotes—I read all of that and I don't care when the term originated, that's pointless pedantry. The medieval kings thought of themselves as reconquering, so reconquista is a decent word to describe what they thought they were doing, regardless of its origins.
