almost relieving, really

They use rule-based subsystems, but they also use deep neural approaches. The system diagram on their website (in the "How Nibble uses generative AI" video towards the bottom) shows the following:

The "fact gatherer" and "GPT generative atom" components explicitly use GPT. The "NLU Intent and Entity Models" are classifier components that probably use deep neural approaches, but they don't say. It's a good system architecture, it combines the strengths of neural approaches with the strengths of rule-based approaches to address their particular domain, instead just using some massive LLM that tries to do everything.

Of course whether a website actually NEEDS a negotiation chat bot is another question...