Pretty simple explanation, they let the clearly copyright infringing content in to their walled-garden under safe harbour protections, but allowing download is contributory infringement with distribution and there's no hiding from that as they can clearly easily prevent it (as they have). Super hypocritical? Sure. Understandable? Also a yes.
Apollo, one of the best mobile clients for Reddit (highlighted by Apple in the App Store), allows direct download of media from Reddit. If Reddit forces this, I assume browser extensions are the next step that they can’t mitigate. If the browser needs to play it, it can be ripped.
I assume from a legal point of view that is a-ok. They can't do anything about it therefore they can't be expected to do anything about it.