Nevertheless, notice the other example I gave is a United flight originating in Honolulu, Hawaii, transiting Micronesia, and ending in Guam.

It’s the same rule.

That is an American airline flight that starts and ends in the US, therefore complying with the rule.

The rule is simply that foreign-owned airlines can’t fly point-to-point routes between US destinations.

I’m in Chicago, and I can book a Korean Air, non-codeshare ORD-ICN-GUM right now. You can find it on Kayak.

Kayak may offer it, but if you try to book that on the Korean Air website you get:

"This is based on the regulations of the U.S. Department of Transportation and you cannot make a reservation for an itinerary from the mainland U.S. to Guam (GUM) via a third country"

The rule is not that foreign-owned airlines can't fly point-to-point routes between US destinations - Air Canada can't sell SFO→JFK via Toronto, for instance. You may somehow be able to cause something to be ticketed, but that doesn't mean that you'd be able to check in.

It's not a componentized ticket from the airline, but singular tickets that Kayak has joined together. Or, it's simply ignoring the regulation, and will be denied by the airline once you attempt to book it.

As the other poster mentioned, try grabbing a componetized ticket from the airline and they will not book it.