Here's some thoughts on Not!ZK:
1. Zhi over-committed when capturing the Wavecrown (depleted forces and cost you flexibility)
2. The natural wonders have special abilities -- unclear if this is relevant, it may apply to the specialties of Kun and Daiyu?
3. "You play boldly. If you do not disguise your movements, your intentions become clear." and "If your actions are not properly disguised, then the consequences will find you sooner rather than later."
4. Zhi tried to take the Shivering Rapids, but NotZK countered with the Sunvenom Tribe (NotZK mentions that future games, he will know Zhi values the Rapids, presumably meaning future loops)
5. "You used your Night Lurker to slay a few of my Hatchlings."
6. "I was prepared to lose the Sand Nest." and "It allowed me to gain in power early in the game, certainly. It was… useful. But it could not grow to match my needs. I kept it for as long as I did because moving those Hatchlings would have taken time that was better spent elsewhere. Losing them and the Nest is not ideal, but it is hardly a great loss."
7. "And though [taking the Sand Nest] is inconsequential, it was still unpleasant."
8. "Our game has been enjoyable in its own way," the figure masquerading as my friend states. "I have enjoyed our time. But every piece reaches the end of its usefulness- and some must be cast aside before they can truly be used."
The named entities are the Wavecrown, Shivering Rapids, Sunvenom Tribe, Nightlurker, Hatchlings, and Sand Nest.
The Wavecrown may be the kids in the first loop? As for the Rapids and the Sunvenom Tribe, that might be referring to the kid Zhi was chasing at the end of the first loop, and whatever killed him? (Assuming he died at the end of the first loop.)
The Night Lurker may be Zhi himself, interrogating the weaver? Unclear what the Hatchlings are.
I suspect the Sand Nest is referring to the weaver, since Zhi taking it was "unpleasant" -- possibly referring to the kukui(?) being forced to erase her from the loop?
But it's odd because the kukui seems to view Zhi as having done something to his forces -- not just the weaver herself, but whatever the entity set up to defend her.
So is the Sand Nest the entire village? And the Hatchlings the villagers, or possibly fake entities sprinkled among real villagers?