In woodworking, that's a different word. In "english" English, the woodworking word is prononced "raowting", as in "now" or "about"; the business of choosing a route is pronounced "rooting", as in "boot".
In American English, "route" and "about" have the same vowel-sound, which seems unfortunate; I wonder how that happened.
English is a mess, but I hope we don't try to fix it!
Sure, most of us understand there are different uses of the word "routing" with respect to technology stacks. But they specifically say "Internet Routing" in the article title and elsewhere. "Internet Routing" does have a fairly specific meaning i.e. IP routing as define by a bunch of RFC's. What they're doing isn't really "internet routing", it's really just redirecting traffic.
Why? It is a perfectly legitimate use of the term. You can use DNS responses to route visitors to the appropriate datacenter or regional network.
Head over to https://cachecheck.opendns.com/ and plug in 'www.google.com', you'll notice the Google returns different IPs in different geographic locations to route visitor traffic.
When an expert is explaining things to non-experts (like a marketing page would), you use terms that your audience will understand and relate to. The goal is not perfect technical accuracy. The goal is to convey the basic idea so the reader can understand it.