It's certainly not unheard of for ports to be farmed out. Considering the massive differences in architecture and the fact that Blizzard probably had little experience working on the PSX it's highly likely that it was rebuilt almost entirely by a different team. Given that most current consoles are x86 machines and multi-platform engines like Unreal and Unity, PC and console versions of games are much more likely to be extremely similar.
I think that's what they mean by not compatible. Diablo's PC controls aren't really conducive to being mapped onto a controller.

Let's not forget D3 being a PC game, the 360/PS3 port had massive changes in order to make it usable via controllers.

Just saying it's more than just mapping.

Because controllers were used on consoles as a consolation. They didn't WANT to use controllers but KB&M wasn't an option to release on PS1. So they had to concede to controllers to make those 7 PS1 sales.
Hahaha. What a fail. Console Diablo was better than PC.... That's truly laughable. I own more PC copies of Diablo than they moved on the PS1.

Congratulations, you reiterated my point!

Now, I don't use xpadder or similar software, so I don't know what features they provide, but I assume they primarily map controller inputs to keyboard input.

Diablo requires a mouse-like device since you move by clicking at he point you want your character to move to, you can't use arrow keys or WASD to just move in a certain direction.

Perhaps you can map an analogue stick to mouse movement and two buttons to left and right click, then you could use the stick to move the pointer and hit the "left" button to tell the character to move. You'll most likely have great troubles with not being able to react quick enough when being swarmed by enemies.

The Diablo source code was leaked or reverse engineered so maybe there is a fix.

Maybe it is possible to use something like cheat engine to hack the game to give controls like that.

That could work but still wouldn't solve the problem pointed by Maighstir. The game is balanced on the assumption you're able to react as fast as a mouse allows you to. Moving the joystick in a approximate direction isn't nearly enough: your character won't attack the skeleton right in front of you unless you position the cursor right on top of it and click. When you're being swarmed by a bunch of them a fast aim is crucial.
I'm sure you're going to start finding your enemies become tough much earlier with a joypad than if you were playing the same level with the mouse.

 
When Diablo was released in 1996, controller support on the PC was largely considered a novelty feature for arcade-type games. There’s no technical reason why controller support couldn’t have been added later. The main reason was simple cost-effectiveness. There has never been a significant enough number of people demanding controller support for Diablo 1 to justify the cost of adding it. Yes, Blizzard could make an update now that adds controller support. But the few extra sales it would generate would in no way justify the massive expense in doing so. And just because there was a version of Diablo on the PlayStation 1, that doesn’t mean you can just pluck out the controller code from that version and plop it into the PC version. Consoles are not just “PCs with a controller”. Granted, they’re getting closer to that nowadays, but if you’re talking classic games from the 90s and early 2000s – PCs and consoles from those days were as different as night and day.

Bottom line: it wasn’t built in initially because there wasn’t any demand for it at the time. And it hasn’t been added in now because the cost of doing so isn’t worth the effort. And, honestly, there’s probably no one left nowadays who even remembers the original code well enough to do it and – more importantly – properly debug it when it breaks other parts of the game.

My solution is different to Maighstir.

My solution would make moving the stick left or right, move your character by using whatever code makes them move when you click on the screen.
Mobs and items would be selectively targeted with some target buttons which is why I mention WoW style targeting in my earlier post. In that game you could quickly autotarget and cycle through enemies you were fighting without having to click on them.

You have no idea how much code has to change in order to make this modification. It is anything but simple. You're basically throwing out the whole gameplay code and writing new one from the zero.

If we were in the year 2000 and you were giving this task to someone who worked in the game during the whole development cycle it would already be a big task. And that's supposing the game's code is extremely well documented and organized, which it usually isn't in the game industry due to the short-sightedness of managers who have no clue about games or how development should be. In this industry projects are very expensive and there is a heavy pressure to release something ASAP that is not so heavy for companies that develop for other industries. Game development time is always very short and the dev team is driven to cut corners all the time.

If it wasn't enough in the case at hand you're assigning this task to someone who doesn't have knowledge of the code, much less a fresh one, who may possibly not even have the original source code and have to work on a decompilation. Decompiled code is recreated very different to the original source. All elements inside are "renamed" (with random names that don't indicate what their content or purpose is) and the code is stripped of comments. In my most optimistic nearly-utopic views I can't see it taking any less than 6 months to just start (roughly) understanding what areas of the codebase this dev is supposed to touch and which ones are not related to the task, like sound, graphics or file management.

All of that time spent in this new feature is obviously costly. Do you believe the extra feature will bring enough revenue to pay for it or are you going to pay out of your own pocket?

Edit: I forgot to clarify: moving your character around could indeed be simple. To change how targeting works, however, definitely would not!

Edit2: I also forgot to mention that after you modify that much gameplay you can expect you'll need to work a lot rebalancing the difficulty. Throw in another several months for this extra task.

There is the Devilution project, which has recreated Diablo from debugging symbols, and an such is effectively an open-source version of the Diablo source code (just the game logic, you still need the assets, which coincidently can be grabbed from your copy of the game here from GOG - or your original discs, whatever).

I don't know if the author of Devilution have added any functionality such as gamepad support, but the possibility is there.

You're over complicating the issue. It wouldn't surprise me if some modder fixed it because it would make the game more fun.

People have made aimbots, AI players and leveling bots without even having source code. Why would something like this be so hard.