From the article: This means that all dialects are separate languages, at least according to this article's knowledge of linguistics. I don't know if that's true or not, but they are definitely arguing that AAVE is a dialect of English and also stating that all dialects are separate languages with influences off of their base language.Linguists never say things like "This is just a dialect, not a language." Rather, they refer to one language as a dialect of another.
No, that's not what it means at all. They aren't arguing there in that section that all dialects are separate, they're saying that "dialect" and "language" are classificatory terms that aren't inherently judging. That's why they go on to explain how nationalism can influence that classification. You yourself could make the argument that all varieties of a language count as separate languages, but the article I posted does not.