It does seem confusing but:
You'll need all the demographic info of the YT when making the reservation, but no proof of guardianship is required. You need this anyway for all travelers, no?
Bringing a copy of the itinerary is always smart, especially for the YT. Also helps secure the gate pass too if you choose to escort.
What is not explicit, nor explicitly prohibited, is if the YT shows up at the counter alone to check in. Or the TSA checkpoint.
I think that is the real question Mr. NoStressHere.
Since they lump the 12 to 18 yo YT together, I'm guessing they can be alone if you choose them to be. They are not going to get WN support anyway.
They few times I did this for the younger end of the range, I escorted and waited for my own comfort but don't recall anything was required.