NameCheap overtook Go Daddy for the author. Search results change based on location, your preferences, search patterns, and just about everything else. One search does not a ranking change make.
If you log out or search in Incognito Mode (basically stripping out that personalization data), NameCheap does show up first for the term "domain name."
> (basically stripping out that personalization data),
Except for your IP address, along with all of the information sent along in your user agent string (browser, operating system, etc....)
I don't know how Google takes advantage of any of that, but I wouldn't be surprised if there's no real way to get a 'canonical' unfiltered search at all... and even if you can, it makes this kind of statement 'X overtakes Y' rather meaningless if most searches have the potential to be so heavily filtered/bubbled.
Sorry, I meant #1 as far as actual domain name registrars go.
Namecheap was #2 and GoDaddy was #3. I think the author was referring to the fact that while Wikipedia has always been #1, GoDaddy & NameCheap had switched spots.
As I mentioned, I used a different computer to see non-personalized results. You can check it out on a proxy search tool like NewIPNow.com to see unpersonalized results.
Incidentally, I have 100+ names at Godaddy and bid on their auctions, while I do not have an account at NameCheap.