If I'm being generous I would say it's "funny" that for all the talk about how 4e had no association with WOW or similar games and anyone who says otherwise is must be an idiot or a horrible person, that almost all the comparisons I heard at the time were from people who liked WOW and 4e.
Heck, the Podcast I listen to that still plays 4e you can go back and hear episodes from back then and the WOW player is like "This is just like WOW!" and the GM uses comparisons to help players understand concepts (an encounter power is like your "cool-down"). I guess they are all just idiots.
Personally, I think there is a comparison in the sense that WoW is unabashedly a game first, and an RPG second. 4e is also unabashedly a game, and it handles the fiction and the things which happen within the game in a way that makes a good game. The game side of other D&D editions has always been much weaker and treated almost as a secondary thing (though I think 5e is certainly closer to 4e in this respect than previous editions, it still insists on a lot stuff that doesn't really work well at all from a game perspective).
This made 4e inherently very playable and pretty easy to learn. This is particularly why it is widely considered to be the best edition to DM, because the structure of the game, the way things work in 4e, even its lore, is intended to make DMing easier and more fun.
So, you can compare WoW and 4e and say that they both approach RP from a 'gamist' perspective. Still, it is VERY true that they are nothing alike in their details. I think 4e designers looked at WoW and other online games and then went back and had that information in their minds when they came up with goals and processes for the design of 4e, but they didn't carry over any of the particulars. As others have said, 4e's roles are NOTHING like their WoW equivalents, but 4e clarifies how classes and parties work by leveraging the role concept into an explicit framework.
This is, frankly, the main reason to like 4e. Whenever it does something, the design is intentionally organized around "what will play well?". Think about teleportation. In previous editions this ability is practically game-breaking at higher levels. It creates a very difficult situation for the GM in terms of presenting some fictional limitations and obstacles for the PCs. OTOH 4e teleportation has none of this issue. You can teleport, by engaging in a fairly lengthy ritual, which will only take you to a known point, a teleportation circle. Yeah, the GM could place one of those in the bad guy's lair, in which case it is just another dungeon entrance. He can place one in the PCs base (or they can build it themselves) so they can 'bail out' if they have time to cast the ritual. It doesn't allow for almost-arbitrary travel and surgical strikes that bypass every obstacle and undermine the paradigm of the game. There is also 'tactiportation', which is just flavor for a nice move option (can cross most kinds of terrain and avoids OAs). These aren't even particularly narratively inept mechanics, there's plenty of high fantasy where things are equally limited and its not like teleporting is even possible in most fantasy fiction at all.
But far beyond that, the very processes of the game are friendly to telling a story. Skill Challenges allow measured progress that lets the players know objectively what the value of a given tactic is, whereas in a game like 5e who knows? You make a skill check in 5e, how much progress did that represent towards your goal? As much as the DM felt like it being. So how can you know if it was worth the cost? You cannot. In 4e I'm in a Complexity 1 SC, that success is 25% of me achieving my goal.
If I had learned anything of value from the edition wars, it would be how different people actually played D&D.
