So I went in and blasted through the Darkening of Tristram, Diablo III's 20th anniversary event. This essentially recreates the original Diablo in Diablo III's adventure mode, doing some fun things like pixelating the graphics, changing the UI, altering run animations and simplifying the sound effects to make it feel more like the game from the 90s.
You can access this by going to the ruins of Old Tristram in adventure mode, where you'll find a portal transporting you back.
It's then a linear (for Diablo) trip down through the depths of the cathedral.
There are four bosses, The Butcher, the Skeleton King, Archbishop Lazarus, and the Dark Lord himself. The first two bosses can be missed - I didn't actually see the Skeleton King on my run - but Lazarus is required to get into the final level where Diablo is.
I'll confess that I find Diablo III's endless hack-and-slash gets a little tiring after a while, and given that this is recreating a 20-year-old game of the same sort, you can imagine that there's not much in the way of... plot?
Actually, when you beat Diablo, the old cutscene from the end of the game plays (with 90s era CGI,) which involves the Warrior plucking the gem from Diablo's head and putting it in his own head. What I do not understand is who the human who had had the Red Soulstone prior to this was. We know that the Warrior was the prince (and became the Dark Wanderer/Leah's dad) but this guy can't be Lazarus or Leoric, as both are already accounted for as earlier bosses.
You can get two in-game pets. One you can get after a little quest that starts with you getting a Rotten Mushroom from level 9, after which you can go around the ruins of Tristram and basically trade items between various corpses (reviving them as ghosts) until you get a recipe to craft Wirt's Leg. Crafting and then immediately salvaging it will give you a guide regarding three cow corpses next to Adria's Hut (in the flashback) that will open a path to a farm where there is a cow pet in a chest (don't click the cows until you have the guide on which order to click them in.)
The other pet, which I didn't get as I took my best-in-slot level 70 Crusader through, requires you to go in at level 1 and complete the event, which yields a little Butcher pet.