I will be testing this in a few weeks. I'm on a flight to Mexico in paid first class. The old language and new language are essentially the same. So far as I'm concerned, I'm traveling on a Skyteam flight. The language even links to a "list of Skyteam member airlines" and (of course) Delta is on that list. If they meant to exclude Delta "skyteam" flights they should have said so.

Is it a big deal? Nope. In the scheme of things, it's definitely a first world problem. However, having lounge access on the outbound flight is one of the reasons I choose to pay for first class. It's gonna suck if they now decide that I don't because it's not Delta One, although it is a Skyteam first class international flight.