Gee, that kinda' undercuts his argument that he declassified everything.

It's far worse than that for Trump, if the description of the tape is accurate (which it might not be).

Trump's claim that he had declassified everything was always a bit farcical. His strongest defenses against criminal liability were elsewhere, particularly in the intent requirements for the statutes in question. To get a criminal conviction under many of these statutes, prosecutors can't just prove that the documents were classified and in Mar-a-Lago (which is easy). They have to prove that Trump was aware that documents were in the boxes at Mar-a-Lago that shouldn't have been, and that they hadn't been returned to the government upon demand.

That's not easy to prove, because the actual handling of the boxes and the papers within them would have been mostly handled by third parties - staff and lawyers and others. It's hard to assemble proof that Trump was actually aware on an ongoing basis of the specific contents of the boxes and documents and that the retention of documents was willful on his part - rather than simply a mistake or oversight or criminal activity committed by staff and not Trump.

With a tape that had the discussion as described in the article, though, Trump is in a lot of jeopardy for violating 18 USC 793(d), which makes it a crime for:

"[w]hoever, lawfully having possession of, access to, control over, or being entrusted with any document, writing, code book, signal book, sketch, photograph, photographic negative, blueprint, plan, map, model, instrument, appliance, or note relating to the national defense, or information relating to the national defense which information the possessor has reason to believe could be used to the injury of the United States or to the advantage of any foreign nation....willfully retains the same and fails to deliver it on demand to the officer or employee of the United States entitled to receive it;

Note that for this statute to apply, the person has to willfully retain a document relating to the national defense upon demand. They have to know they obtained lawful possession of the document, know it relates to the national defense, know that it has been demanded by an officer or employee of the U.S., and know that it was not returned. It's hard to prove that - because you have to prove what Trump actually knew and when he knew it. For any random document in a box in a storage room in a vault, Trump could (quite credibly) just claim he had no idea what specific papers were in there - and that he thought all the important stuff had been returned already.

If they've got him on tape accurately describing the contents of a document relating to the national defense and stating that he still possessed it on a date after the subpoena, though, he's in real trouble. Because now they've got some proof of specific intent. It demonstrates that he was aware of that specific document still being at Mar-a-Lago after it was demanded back by the government.

That, more than puncturing the ridiculous de-classification defense, is the real damage to his case the tape might do.