"Other games" (plural) didn't kill EQ. DAoC, Asheron's Call, Anarchy Online, etc., were small potatoes. WoW killed EQ. Hardly surprising as that was exactly how it was designed: as a non-hardcore EQ. You no longer had to stay up an extra two hours on a work-night to arrange a corpse-run, and so on.
No, EQ was already in trouble nearly a year before WoW came out.
They fucked up with Gates of Discord in early 2004 which caused a lot of problems. Even before then, there was discontent in the community about the direction that the expansions were going in, such as Luclin having alien looking mobs to fight that was moving away from a more DnD-like fantasy setting.
This was the time when they were inviting the major figures in the leading raiding guilds to talk about what needed changing.
It was during all this trouble that WoW emerged on the horizon and people tired of Everquest began to look to it as a better prospect. Fires of Heaven and some other major guilds were upfront in abandoning EQ for WoW because of it's issuesband WoWs promising development.
The issue with EQ was it wasn't built to grow in the direction that it later went into with raid content. When Everquest came out, even the devs had no idea about raiding and had very weird ideas around how early raid targets would be handled, and indeed, how group encounters would be, too.
Splitting groups of mobs with Monk FD was originally seen as an exploit and was punished because it was a player developed tactic the devs never considered. It was later a concession that they went along with that resulted in Monks becoming the main pull class when originally they were simple DPS.
Crowd control wasn't an original idea, either. Enchanters were originally to be the pullers and do so with mez. Clerics too with their lull line of spells and an added reason for them being a plate class to soak up damage from aggroing. Using mez to lock down mobs in fights was something players, again, came up with.
For raids, CH heal routines were never considered. CH was designed as a between fights heal to top players off, not one players would use in battle, much less chaining Clerics together to keep a Main Tank with it, which is why it never had a successor spell once players HP went above it's 10k heal max. Verant seriously expected non-CH healing to be used for fighting the first dragons and gods.
Everquest created MMO raiding.
The issue with that is the itemization and growth in stats wasn't made for that in the beginning and it peaked with Velious before becoming ludicrous by Luclin. The itemization growth curve and raiding ruined the PvP servers and ultimately ruined the entire game because it destroyed the culture the community had created.
WoW was made with a more clear idea of what it would grow into and came with EQs lessons built into it mixed with a wider vision ariund it's scope and growth potential.