That's not what's being talked about. Eudaimonia refers to the benefits of living virtuously, a core part of Stoicism, but not the part that's directly being discussed in this article. The ideas discussed in this article are about self-control, disconnecting your emotional well-being from things that are beyond your control, and seeking happiness from within. Those are quintessential Stoic principles. A lot of the modern pop-stoicism also delves into the benefits of virtue, maintaining the connection to eudaimonia and Socrates' question, albeit in a slightly round about way. The only Stoic principle that's usually left out of these discussions is pantheism.

> similar notions pop up all over the place in ancient philosophy

You're right, they do. That doesn't make them any less Stoic though. Perhaps if this was a Chinese message board, we'd all be talking about Buddhism instead. The two philosophies do have a lot in common.