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.