I'm not variant, but I have played a few MMOs, including World of Warcraft, and I don't really see the resemblance. There really are not that many mechanics that are distinct to 4E that are seen in any MMO. I'v never heard of an MMO with anything like marking, healing surges, the standardized power system, the short/extended rest system, or pretty much any other such thing. On the other hand, 4E doesn't really have many of the key features of something like World of Warcraft, such as its convoluted loot/crafting systems where every character has two harvesting or crafting skills, an aggro mechanic, solo/group/raid tiers, large class talent trees, cooldown and fatigue/mana mechanics for skills, skill "proc"ing, etc.
I mean, you can vaguely say the two are similar because they both have class roles, but even that implementation is wildly different. 4E has four roles with a lot of conceptual overlap, every class has a single role, and most roles have distinct mechanics (like bonus damage, "word" healing powers, and marking) to distinguish them. WoW has three roles which have very little overlap, many classes can take their pick from a few roles, and there are no clear mechanics that are the same across all roles. It is the same concept, but very, very different in execution.
In terms of flavor, WoW and 4E D&D really are not alike in the least.
I honestly have never understood comments that 4E is somehow built entirely to appeal to WoW players, considering that it doesn't really do much to do so. At the very least, I would expect it to have playable Orcs and gadget-loving tinker Gnomes if it were going that route. And of course, WoW has nothing at all like Dragonborn, so 4E's most visible race differentiates it from WoW, rather than indicating similarity.