Except not? None of their demo images on the website show strong noise, mostly medium to low noise.
Their wording could use some work, though, since it seems the description below all the "Remove noise" examples says: "AI Clear uses the insight of a custom neural network trained on millions of images to detect and reduce noise
as well as enhance details in your images automatically." and that sounds about the most correct.
Even in their specialized noise product: https://topazlabs.com/reduce-noise/ which has "Reduce" in it's name (and works quite well with your image, btw) they jump between "reduce" and "remove".
As far as I know initially AI Clear was built to do exactly what is stated above, but sounds like most users expected it to deal with much more image noise, so the Medium and High models were added (relatively recently). I'm sure they will keep on "training" them and improving the results.
For what it's worth I tried AI Clear with the image you attached here and did not get splotches of noise throughout the background, but several spots on the edges weren't perfect. Might be due to the resized image.