In the U.S., yes. The (HTML, CSS, XML, PHP, etc) code that is used to design a website, or any attribute of the same can be copyrighted. The cost varies and the copyright ownership lasts for 70 years past the owners death, but can be transferred to a new owner (similar to selling your car).
Here's the thing. Adding a claim of copyright on your website
Copyright © All Rights Reserved isn't copyright protection. You actually have to file the code with the Library of Congress, make your payment, and keep your copyright document safe enough that it doesn't fall into the wrong hands. So, if the site, who is offering a license for their icon set, has not filed the copyright... you can do it (thereby stealing it out from under them). Then you can force them to stop selling a license to the icon set that you (effectively) own.
If, on the other hand, they filed for a copyright to protect the icon set, and according to the Copright Law of the United States of America (circular 92, which I obtained online through the Library of Congress):
§504 a) ... an infringer of copyright is liable for either--
- ... actual damages and any additional profits..., or
- statutory damages, as provided in subsection (c).
Subsection C goes on to indicate that damage ranges between $750-$30,000, but that it can go as high as $150,000USD. Of course, it's not unlikely for courts to add attorney fees and court costs to those figures.
So, it might be worthwhile to do some research and find out if they own the copyright or not. If they do, $25 is a lot easier to pay than the potential $150,000+. It's a matter of how far you want to take it.
Note: Your website's copyright is essentially a copyright to the way you used the code to represent your site. So, you don't own HTML or any other language (unlesss you create one and then copyright it). But you would own the way you used it to represent the website to the viewing public. So, this person's CSS code could be copyrighted in that it created the icon set. My website is different because of the way I wrote it, etc.
Words, btw, cannot be copyrighted. Or trademarked. A trademark is (essentially) an image of a word (like a logo), but the word by itself is under public domain and available for free use.