As someone that used to play every FF game that came out before the spinoff stuff happened with XIII and is somewhat of an MMO aficionado, it isn't really so much influenced by any single solo player Final Fantasy game as it is a cumulative product of decades of design decisions, gameplay mechanics, storytelling devices, and so on.
The largest clear influence to me is Final Fantasy XI, which I still think has the best storytelling in an MMORPG. XIV doesn't shine as brightly to me, but it still carries the same flavor, with more humor in my opinion. Other clear MMO influences are World of Warcraft and adapting several smaller but exceptional elements from otherwise underwhelming or forgotten games, like the FATE system being almost a direct lift from the titular Rifts in RIFT.
It isn't just WoW with a Final Fantasy skin, which I think a lot of players superficially make as their first impression. It does have a lot of very carefully crafted Final Fanservice in terms of how things look, though. It has what I consider to be the hallmark of a good and lasting MMO; crib what works in other games, make it uniquely yours, and make it work within the framework you created. That's how WoW got started, too.
The ties between XI and XIV are so strong that XIV can be enjoyed on a second layer if you did play that, but you won't miss it if you didn't.