If more than 2 players can play at the same time online, it's a MMO. A MMORPG is only different by how much distinction is made between the PvE overworld and the "hub" city there is. PSO2 is also a MMORPG, but 100% of the game is instanced other than the hub world. That was also how Wizardy Online works, that's also how Vindictus works. Games like Fortnite, Pubg, Team Fortress 2, etc create instances for the fights to be played it, that is no different than how FFXIV or WoW's dungeon instances work. Nearly every MMO Shooty game has the exact same RPG progression system of upgrading gear makes you better, while not all of them opt for "levels" or "experience.
The thing FFXIV, and only FFXIV has going for it is that it is casual friendly by having no full-time PvP at all. Games that have perpetual conflicts fueled by PvP or PK'ing hinder PvE progression. That's why open-world PvP gets shouted down, don't ruin the thing that makes this game appealing.
Trying to make a distinction based on the presence of storyline or rpg elements does not make a game any less of a MMO, it just makes the development costs of the MMORPG greater than that of a F2P shooty game that doesn't need to write any story to justify flooding the game with microtransactions.
