On one hand, yes, the author was using Waffle House's own data to populate the site. But on the other, Waffle House has no way of guaranteeing that remains the case, and they don't want their private APIs to be depended upon by a 3rd party site seen by thousands of people. So I guess I'm not surprised by their reaction. Still: it would be fun if it actually was a thing.
It's a trademark thing, brands are really protective of them because the rules around dilution are a bit murky so they err on the side of trying to stamp out any unauthorized use just to make it clear it's in use and protected so there's little chance of losing it because a court takes a different view of a time they let it slide.
Waffle House also has an interesting history with trademark protection and dilution. The company started and expanded when trademark protection involved more per-US State registries than it does today. In Indiana for a couple decades the Waffle Houses there were known as Waffle & Steak, because a home-grown Indiana company was already known as Waffle House there. Sure, Waffle House does serve Steak (though many don't realize and wouldn't think of Waffle House as the first place to go for a Steak), but it wasn't about marketing their non-Breakfast menu items (they have burgers, too!), they wanted to protect their trademarks on the signs and other parts of their branding, even in states like Indiana. Steak has 5 letters like House, that was the important part. The signs looked clearly enough alike from the interstate even if the words were different.
Right, and I don't really have anything interesting to say in that direction. I was more discussing that Waffle House claimed "This information is incorrect. We currently do not have a live website tracking restaurant closures", and the author's response "But I was quite literally USING their data for this, so it wasn’t really incorrect at all."