Submitting other people's work to the arXiv
This should be perfectly acceptable if it is framed as an exposition article. There is a long tradition of expository articles in mathematics (one example that comes to mind is Thurston's exposition of a method developed by Conway to determine if the plane can be tiled by a given shape, see here). Just make sure that the abstract and the introduction convey that all you're doing is to explain Szelepcsényi's proof.