Even after reading the article, I don't understand what one has to do with the other. If it plays single player just fine on the Steam Deck, why can't you play multiplayer? And what does it specifically have to do with PSN? Maybe I missed it, because the site doesn't format well at all on mobile.
From reading a different article on it, it sounds like there's a new PSN in-game overlay that's needed for multiplayer functionality, and it doesn't work due to some lacking windows components. There's a chance that Valve will be able to add support for it in the future.