Also, I wouldn't say the results are nonsensical - I think it has learned a lot more than a markov chain or a simple rnn but I agree that especially on the surface they dont even sound like they surpass Eliza by much. Moreover, it is significantly more apparent how much it learns about the different people you've talked to AFTER you run it on your own data.
For a somewhat more novel/interesting result with fine-tuning GPT, I can recommend checking out gwern's post on training it on a big poetry corpus.
The samples also looked a lot better than OP's. I assume that's because he ran it for more like a day on a few hundred MB of chat logs.
Personally to me it reads like it could fit in written by someone disgrubtled in IT mocking the blatantly unqualified nepotism installed morons who they have to work with. It could be embedded in an "Office Space" style novel as actual chats between "worthless heir brigade" being eavesdropped.
It is passing Turing in the same sense spamming random keys based upon virtual keys on a keyboard and alternating silence and way too many messages seems like a real totally illiterate toddler got a hold of the keyboard for a bit.