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.

It was not awarded because that paper is on arxiv. That paper could have been printed and sent out by mail. Or posted on 4chan. etc. It just so happens to be it was on arxiv which made no difference to anything.