I would say it's released in the spirit of machine learning's competitive landscape (which is the culture this emerged from).

So they could also dump a 100 quadrillion line proof in Bourbaki notation and call it a day?

The proof was released in the spirit of being first at all costs without any attempt to clean it up. I doubt that OpenAI mathematicians could give a coherent talk about it, certainly not using a blackboard.

What kind of prestige? Peer review is anonymous unpaid work.

A good review does not merely check the correctness of logical arguments, it gives suggestions for the exposition, citing the correct references, putting everything in the right context, etc.

This is an equivalent of a company producing security software, open sourcing their code, and then claiming that since no one has found any serious bugs, their software is secure.

No. The way to build confidence that your software is well made, you do a proper external security audit and obtain the requisite certificate from a proper auditing firm.

It's also incorrect to think peer review in mathematics is low quality (like it is in some other fields). Certainly, when major results are in place, editors ensure that high quality peer reviewers are recruited and do their job properly. Like all human processes this fails sometimes, but not enough to not do it.