Guess i got carried away. Also TLDR post incoming because I love this topic so much.
Then again, the whole reason why I did mention League was that although it is a Multiplayer game from the get go, LoL back in the olden days of 2009-2010 wasn't really a big esports hit. Riot worked hard on making sure it was given a lore that made sense and made you feel that you were a part of the experience, whether you just wanted to play for fun or play competitively. Olden days of LoL had a lot of emphasis with lore such as weekly Journals of Justice, much more detailed character lore backgrounds, readings, extra materials, and stuff. It even made sense on how a character in game speaks to you like in your typical RTS game. (Summoners and their champions have a mental telepathy link between each other) Heck, i remember whenever a new champ was introduced, they were even given another lore reading for people detailing how they were accepted in the in-lore storyline. Even though it was a multiplayer game from the get go, it had a lot of stuff to enjoy for those not interested in being the next esports superstars. Its a much different League since 2012 and after Season 2.
Regarding the "issue" with Fighting Games, i pretty much am spot on with the competitive or multiplayer focus. After all, Fighting Games were never meant for that immersive story experience or anything like that. Its all about beating whoever you face, climbing that ladder, become a member of TSM or IMT's fighting games division, and face off against Koreans and Japanese in EVO or SBO, beat Daigo, Momomchi, Chris G, and their future children, and all that. I pretty much saw SF5 coming out of dat delicious multiplayer focus ever since, and you got Combofiend who worked on that game as well.
Now on to the spirit of the topic:
So it boils down to the game in question.
This pretty much seals the whole argument in a nutshell for most part. I mentioned for the most part is that MMORPGs are another big issue, at least in my view, regarding the whole PvE vs PVP/Multiplayer delivery.
Again, i pretty much endorse competitive multiplayer at this point in time. I mentioned before, sometimes just PvE isn't enough these days. There's always that moment where anyone wished they could prove themselves to be better than others in a game with the simplest way to prove it -> Good ol' fashioned player vs player.
Now anyone remember Ragnarok Online?