He isn't confusing the terms, he's just using the correct one.

Functional programming is about programming with functions - "Purely functional" is redundant. It should be obvious that Functional means functions, and "function" has fairly precise meaning which predates computation, and certainly didn't include anything about side-effects. Languages which don't use functions are not functional - they would be best described as psuedo-functional, nearly-functional, or mostly-functional, as he uses in the article title.

The only reason we've had to invent new terms like "purely functional" is because the original term has been abused to mean what it never meant - it was used to describe psuedo-functional languages, so we needed a new term to distinguish the two.