The restaurant is independently owned. Disney ended up involved because their website listing (which again, is subject to the same blanket TOS as the rest of their online services) had incorrect allergy information. Disney's response, tone-deaf as it was, wasn't wrong: you're supposed to verify with the allergy accommodation information with the restaurant.
Which was not the case here.
It was not a Disney owned restaurant - Disney's involvement was limited to incorrect information on their website, and their TOS basically laid out how that is to be handled.
The plaintiff had every reason to sue the restaurant for negligence, but to sue Disney would be like suing Facebook because someone in the marketplace sold you a counterfeit iPhone. Maybe you'd even be successful if could if you could prove that Facebook knew the seller was selling counterfeit goods, but again, there's usually a clause in the TOS that says it's on you to verify that you're trading with someone trustworthy and if you get screwed, your legal bone to pick would be with the seller.
In the grand scheme of things, what probably happened here was that the lawyers figured Disney would just fold and settle, which is entirely why Disney comes off as being asshole-ish in these types of situations, otherwise you'd end up with every person who slipped on some spilled popcorn in their theme parks trying to score an easy payday.
I'm sure there's some similar dynamics at play with suing OpenAI. You usually don't hear about parents suing when their teen unalives himself with a rope bought from Walmart, but this is new untested ground and there's the possibility that people might be more sympathetic to punishing an "evil" AI company, more so than the store where they buy their groceries from.