Referrers are a part of the way the web has worked since before Google existed. They're a browser-level feature more than something related to specific websites. But if referrers bother you, just use the SSL version of Google to prevent referrers from being sent to http sites (or change your browser not to send referrers at all).
The corresponding sentence even for a website that strips referrers would be "When you search on domain X, and click on a link, your browser & computer info is sent to that site, which can often uniquely identify you."
Read more carefully in that light, the first sentence is really saying that third-party sites that you land on after searching or visiting a domain can track you. That's independent of whether you came from Google or any other search engine, of course.