Retrospectively, if the game was an original IP from a studio unrelated to Zenimax or Bethesda, but was overall the same game sans iconic locations from ES lore, I personally would still play ESO knowing what I know about it today.
However ESO being an Elder Scrolls game is what drove me to pre-order the imperial edition when the game was announced. I played the beta, played with my wife in the beta once or twice, and picked the imperial edition up from Game Stop the day it was announced. I seriously doubt that I'd have ever even considered ESO if it wasn't an Elder Scrolls game. So retrospectively, yes, it's my favorite MMO and does not need to be an Elder Scrolls game for me to like it. But no, I wouldn't have tried it because it would have gone under my radar if it wasn't an ES game.
Before ESO, I avoided MMORPGS entirely. I was always more of a single-player type of player (and in many ways I still am, I fly solo almost always even in ESO) - I had no interest in World of Warcraft, and past flirtings with Everquest and Ultima Online rarely got me past the character creation.
But because I was heavily invested in the lore and world of The Elder Scrolls Universe, when the announcement came about an MMO in mid 2012, I was a bit intrigued. Skyrim was still fresh, so a new major Elder Scrolls game being announced less than a year after Skyrim was a surprise.
Yet I was initially not really sold on it. I think I needed to see more of the game for myself before I made any kind of decision on it. There was no confirmation of whether there was first-person in the game yet, and I felt that the lack of such would not make it feel like Elder Scrolls.
I think what ultimately sold me on ESO, besides it being Elder Scrolls and the confirmation of first-person mode in a trailer released (I think) around mid 2013, was my experience during the closed betas. I had fun, I even ran a dungeon, I felt the combat style was immersive enough, and first person mode made it feel pretty close to a traditional Elder Scrolls game. Now, I have 2/3rds of an entire YEAR of play-time on just one character, and a few months of in-game time scattered among my alts. It's been my go to when I need to just relax after a long day, or take my mind off of things that are stressing me out. Achieving things in game feels rewarding, like when I finally got Emperor a couple years ago. I'm currently in the final day of the absolute craziest trader week in history (at least for me).
I don't think I'll be stopping any time soon, honestly.