1. As with most things, being first (with a big following) out of the gates is a huge factor for all things. Now there were certainly other isometric arpg's before (diablo I for example), but Diablo II was probably for many people their first real experience with such a varied (builds, content, items!) game. All similar games that have come since have had to compare to Diablo II, no-one says "but it's not Nox/Titan Quest/Torchlight" when new aRPGs are released, everybody compares games to Diablo II. And with such a legacy and hype, to this day, still new people try out Diablo II based on these kinds of comments and love it.
Now as I said, it's not necessarily the first game that becomes the standard with which all subsequent games get compared, take Wow for example, it was certainly not the first mmorpg, but by god (or zod?) did many people play it propelling it to become the staple.
With that said, without the next 3 points, the above would be moot as some other game would have overshadowed Diablo II and taken the throne as the early standout staple game.
2. I touched on it before, but the itemisation. Not just the well thought out interaction between builds and items, but also the underlying systems for determining what can drop/be gambled/be crafted where and with what character level. The depth to the whole thing makes it huge. The intricacy of this still baffles me weekly.
Also within the context of itemisation, there is always something to improve.
3. Builds. Well, without the build diversity being as great as it is, we would all have gotten tired of the game a long time ago. I think the complexity that was added with skill synergies and oSkill runewords was what actually breathed new life into the game and made it viable for decades to come, without those two changes I think the game might have slowly faded away (albeit, there would still be a following, just not quite as large as it is).
4. I wasn't sure if I should put this 2nd or 4th on the list, but the fact that almost 20 years after release, new things and tactics, and to some extent builds are still being discovered shows us that the guys at Blizzard North really took the time to think things through. Now I realize that some of these things probably are just consequences of development decisions, bug fixes, and side-effects of a game evolving over the years that it was still being actively worked on, but looking at the things that are apparently intentional, my god is it ever intricate.
5. Diverse areas/targets. We have all sorts of runs to do. Straight boss runs (meph etc), area runs (lvl 85 areas), mixed runs (baal, cs), LK runs, Trav runs... And all of them somewhat randomized, for SP we have map rolling which either forces us to have dedicated runners, or reroll maps when we want to switch targets, both of which add longevity to the game. For the online players we instead have the run-by-run randomness.
Honorable mentions:
* There is always something to improve. Even the 99ers we see still could have some charms to replace or some jewels that could be better. There could be some skill tweaks that make running some target more efficient. And being on that subject, there is no character that has a build that is best for all areas of the game within the context of that character. Other games, (I'm looking at you Diablo III), have lots of builds that are viable through the whole game, surely there are builds that are better or worse, but they can all do everything. With Diablo II, some builds are just horrible for certain target while being amazing for others.
* I've always loved how there is a notion of max level, but that it's so far away. Getting to 99 is possible, but most don't get there. But getting there isn't necessary, you can equip most things you'll need for a build earlier than that, but even when decked out in end-game gear, the climb to 99 still gives us something to work toward. Even if just running for mf, with no intention of getting to 99, the exp bar still fills up giving a sense of progress even for those that don't care about it. Add to that the fact that many builds, even if they're "complete" by lvl 80, can still be improved with a few more synergy points or some utility skill that might come in handy in certain situations thanks to not being max level by the time end-game is reached.
Sure, other games have other systems to give us a notion of progress, the paragon system, rifts etc in Diablo III for example, but that still isn't, in my mind, as tangible as the actual level om my character.
Ok, huge wall of text incoming. This is from the perspective of someone who's played Diablo 2 off and on for 20 years, tried some other aRPGs over the years, mythos, torchlight, nox, titan quest being some i've played a bit but not too much, and diablo III being one I've put quite the chunk of time into. With that said, for me, Diablo II is the one game that stands the test of time in this genre. As such, I don't have much experience with other games so this is definately going to be biased and full of assumptions about other games, but hey, it's the internet, we all assume things all the time.
I might have had a different perspective if I had played more PoE as I think that's the big contender, but I couldn't stand the way it felt so I never got far there.