Blizzard have publicly denied that Diablo 3 will be getting cross-play, meaning that either the publication misunderstood something, or the company representative made a mistake. To be fair though - it did sound too good to be true.
Anyway, Blizzard's statement reads, "While we love the idea of bringing our players together across platforms, we do not have any plans to implement cross-platform gameplay for Diablo at this time."
Needless to say, this is in stark contrast with their rep, who stated that Microsoft and Sony are already onboard, leaving only Nintendo to win over. Now it seems thtat the company's representative was stuck in rep-talk mode, characterised by everything being possible and already worked on.
At this point, it's questionable whether Diablo 3 cross-play is even possible, or at least viable, as I'm not sure how would Blizzard even go about technical implementation thereof. After all, the game's launch on PC and Mac was followed up by incremental launches for two generations worth of consoles and I imagine getting them all to work would be a horror story, and even that's probably putting it mildly.
It would arguably give Diablo 3 a new lease of life, since everyone and their dog would surely hop on for a run or two, if nothing else then to give cross-play a run. On the other hand, the solution for throwing in the PC with a few console gens would likely be to cumbersome and probably a bit too late into the development cycle to be investing into.
Nevertheless, if you're keen on getting your fix of good ol' Diablo, you can do so once Diablo 3 The Eternal Collection arrives on Nintendo's Switch on 02 November 2018. As is the case with PS4 and Xbox One identically named editions, you'll be getting the base game, Rise of the Necromancer content pack and Reaper of Souls expansion pack.