The links at the bottom of their blog aren't inline in any other text. They're "clickable UI elements that stand on their own", "in a group with other related [links]". One could easily argue they're more button like, especially the email and call links at the very bottom of the page.
The author is complaining about nobody would understand to click on Accept in their example without having an outline around it and yet they expect people to understand to click on "eMail" and have it open their default email client.
Fair enough – however, links are still not buttons. Links should include an href and add a new entry to your browser history. Buttons should cause something to happen on the current page without changing your browser history.
There is value in differentiating between them.
If a link should add a new entry to the browser history, then their mailto and tel links at the bottom should really be buttons then. And yet we don't see people complaining about that.
Besides that, he's pretty clearly talking about clickable UI elements that stand on their own, or in a group with other related buttons.
Links exist inline in the context of other text.