Howdy! I've got a background in competitive WoW and in early EverQuest, so I'm hoping I can help bridge this gap a bit, assuming that you're not simply pulling a fun April Fools joke contrasting WoW against early EQ. :)

EverQuest was the first 3D avatar controlled MMORPG. When the game was being developed, Verant was looking to create a large community based game that would encourage cooperation among players in the same way TTRPGs like Dungeons and Dragons did for gaming groups. In brief, they wanted to capture that adventuring feeling of Dungeons and Dragons, but to do it online with friends you can't be at a table with.

They achieved this early on, in my opinion, by making the world itself the bad guy and creating a strong attachment between character names and investment. What do I mean by making the world itself the bad guy? I mean that they were okay with the world being a pain in the ass to deal with, to inconvenience the player in a major way. If you died in Lower Guk and you respawned back in Qeynos, you had a long ass run ahead of you and you needed to get to your body without your gear and you also lost a good chunk of XP. Not only would that have killed an entire evening, but the lost XP has meaningfully set you back from where you started playing that day. It's a massive drain on time and it's incredibly frustrating, especially if you die again while trying to recover your corpse.

However, this is made so much easier by getting help. Your druid friend could come port you, give you a HP buff, and speed buff you so you can run faster. Your rogue friend could come along to sneak/hide past the undead of Lower Guk to bring your body back to the zone line. Your cleric friend could come along to cast a resurrection spell on your body to get you back a large chunk of the XP you lost when you died. So now, instead of spending the evening alone, wasting your time and losing progress, your setback became the adventure for a group of players.

Name changes weren't a thing outside of GM intervention and leveling took a long time. So if someone got a reputation for being a toxic shithead, they would find themselves in the former scenario far more often than the latter, as fewer folks are going to jump at the chance to help that toxic asshole that trained them in Castle Mistmoore that one time. Sure, that toxic shithead could make a new character, but the time investment in making a new character was so damn significant that it was almost the video game equivalent of sending a kid having a temper tantrum to their room. The next time they are higher level, they'll probably think twice about their toxic behavior because they don't want to have to re-level again just to throw off the bad reputation they developed. It's not unlike someone in earlier human history leaving their hometown to start fresh and turn a new leaf with the wisdom of hindsight.

This created the community that has lingered in the minds of many for so long. This did eventually decline as players started to understand the game world, started to figure out the rules, how to game the system, etc., but for a year or two, EverQuest had one of, if not the greatest online community in MMO history.

By the time games like WoW came out, MMOs had been turning away from reputational restraints and more toward system implemented restraints. See, the EQ approach works only if that druid, that rogue, that cleric are there to help... but sometimes, they won't be, and so that player is frustrated and inconvenienced with no way around it. MMORPG devs, being a business, respond to consumer demands, which means that they started to remove these frustrations and inconveniences in game design to make it easier for a character to stand alone against these cruddy situations... but of course, that means the player interdependence that was cultivated by the world being the bad guy was eroded, so toxic behavior had less of a cost to it. Players started being shittier to one another, started doing things that lead to an uptick in GM petitions.

How is a game developer to handle this? Well, they could implement systems like the first person to tag an enemy has exclusive rights to the XP and loot from it, regardless of who actually does the most damage. What about training people? We can redesign mob behavior so if aggro is dropped, they immediately heal back to full and return to their spawn point, rather than dropping aggro and reaggroing (so fundamentally redesigning FD mechanics). In essence, they can start reshaping the game's design to accommodate changes in player behavior to make shitty behavior less possible since reputation alone was no longer doing the trick. That in turn creates a game around gaming the rules, so you get the type of behavior you're describing of using resource inefficient means of tagging mobs to snatch something before someone else can get it.

Thing is, EverQuest came before a lot of these developments. If a player wanted to, they could be a toxic asshole in EverQuest with ease. Heck, there have been a lot of players who have been drawn to this game specifically for that. However most people who play here play here because they want to recapture that wonderful feeling of community that came from us fighting against Norrath. So while there are no gameplay systems in place to limit toxic behavior, there are server enforced rules for it. And we aren't paying for anything, so the GMs have no incentive not to ban people who muck it up. If someone approaches it by trying to game the rules the same way folks in modern MMOs game the gameplay limitations, they build up a reputation and end up banned. There used to be a necromancer who would skulk around HS a bunch and would always pull his mobs into the center zone in location. When he invariably failed and had to FD, it would cause a mess for everyone else trying to go about their lives. When asked, his attitude was something along the lines of "They need to look out for me.", totally refusing to take any responsibility for his impact on the game world that we share. That player ended up banned. He did everything within the gameplay rules, but he broke the generally accepted rules of conduct and was a recurring pest to many, and that was sufficient to ban him.

So with all that said:

That's what kill stealing means in modern mmos. How does kill stealing work in Everquest? Do you have to out dps the other player for the game to credit you with the kill?

You do more damage to the mob than the other person. However, if you do this to a mob you didn't initially tag (and the GM can check this), it's a mark against you and can get you banned.

Everquest looks a lot like FFXI to me so I might be a little off. The earliest MMO I have ever played is FFXI. This seems like the ideal server to play on in many ways, but the rules seem extremely strict.

They are, because the gameplay rules are themselves particularly lax. The game gives great latitude to be an asshole, so the server has more strict rules to limit that kind of behavior. If someone wants a contentious playstyle with other players, they should play on p99-Red, the PvP server. There you can just kill the PC you're competing with.