The short version is that there are some really exciting developments here about mRNA vaccines, based on genomic sequencing of tumor cells, that seem to be having a beneficial effect on the dog in question.
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https://www.theaustralian.com.au/business/technology/tech-boss-uses-ai-and-chatgpt-to-create-cancer-vaccine-for-his-dying-dog/news-story/292a21bcbe93efa17810bfcfcdfadbf7

But the meme version of this story is super misleading. The actual work of creating the treatment was done by people, using various tools, and to the extent that machine learning was involved it was in things like AlphaFold.

Also, the dog isn't cured -- even the dog's person acknowledges that.
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As for how ChatGPT was relevant to this? Apparently, the desparate dog owner was apparently using it as information source, and landed on the idea of immunotherapy:
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