A Fields medal was awarded based mainly on this paper never published elsewhere: https://arxiv.org/abs/math/0211159

I think there is a misunderstanding here. Does arXiv count as a publication? Yes, pretty much anything that gives you a DOI does, for example Zenodo. Does it function as a reputable anything? No.

The paper you link to counts as a publication, but its reputation stands on its own, it has nothing to do with arXiv as a venue. Ideally, that's how it is for all papers, but it isn't, just by publishing in certain venues your paper automatically gets a certain amount of reputation depending on the venue.