What if someone wants to enter Thailand on a 90-day non-tourist visa to visit the wife. Will that person be allowed to play in the sandbox?

Yes.

Since the exact requirements have not been published yet it is impossible to answer with 100% certainty, but at the moment it looks like a definite yes.

Yes and bring along your own spade and bucket. 

Pretty obvious that as everything is closed in Phuket the kitty litter option is being set up as a quarantine island for onward transition to the rest of Thailand by those who cannot access via normal routes. Very much doubt if any 'normal' Tourists will come. They have cornered the vaccine market under false pretences all in an attempt to keep the funds rolling into the pockets of the Phuket Milionaires who own the quarantine hotels