Nowadays, if you're not happy with the direction Dungeons & Dragons has taken and you're struggling to find a nice, succinct curse word to describe your disgust, "anime" seems as good as any. Of course, "anime" means lots of different things to different people. Some will be pedantic and point out that "anime," like "pulp" isn't really a genre so much as a medium. Others will instead fixate on stylistic matters, equating blue hair -- "You gotta have blue hair" -- and robot boots with "anime." Still others will focus on common tropes and even (more rarely) content, as if the choices made in any single series were definitional.
I tend toward pedantry myself, so I have a lot of sympathy for the notion that anime should be viewed more as a medium than as a genre. At the same time, I also realize that a medium can nevertheless become so strongly associated with particular styles, elements, or concepts that it becomes a "quasi-genre." That's why we can in fact meaningfully talk about "pulp" in ways that are reminiscent of discussions of genre. (The same goes for "noir" in my opinion) So, while "anime" may primarily describe the medium of Japanese animation, that medium has, over the years, become so strongly associated with the content expressed through that medium that it's not completely illegitimate to use the term "anime" in a genre-like fashion.
My purpose here isn't to lend credence to many of the most outrageous complaints about D&D's having become "too anime" over the years. I don't in fact think that's generally true at all, especially esthetically. In many ways, I think D&D has, over the years, become less like anime than it used to be. What do I mean by that? For me, one of the strongest -- and indeed most compelling -- aspects of anime is its willingness to break the staid conventions of genre. That's why, in nominally "fantasy" anime, you'll see weird "technological" items, anachronistic clothing, and even situations that supposedly don't "fit" into fantasy. And of course most anime, even the most deadly serious ones, include plenty of humor, often of the slapstick variety, as a way to break the tension (in the fine Shakespearean tradition).
D&D used to be like this and, as the years have gone on, it's become less so. I know it shocks people when they first read OD&D and see references to John Carter of Mars alongside those from Middle Earth. The same reaction happens when you first learn of Blackmoor and the Temple of the Frog. The prehistory of the Wilderlands setting is just too much for many to bear. I can't count the number of times I've heard gamers complain about the "silliness" of Murlynd and his six-shooters. Even the supposedly stodgy setting of Tékumel has a hobbit in a zoological park and interdimensional forays to Mexico at the time of Pancho Villa. And then there's Arduin, a game so gonzo that it makes Encounter Critical look almost conventional.
At some point, probably after the release of Advanced Dungeons & Dragons, D&D started to take itself too seriously and ceased to be "anime" in the sense I'm using the term. Many people will make the claim that "D&D is its own genre" and that's true -- now. Back in the wild west days when the hobby began, that wasn't the case. D&D was never about itself; it wasn't self-referential. Instead, it was a heady brew founded in pulp fantasy, but, like the pulp fantasies themselves, was quite willing to beg, borrow, and steal ideas from any source that was handy if doing so made the game more compelling to the referee and players. You have to remember too that "fantasy," as a distinct genre, only really got off the ground after the publication of OD&D. Prior to that, "fantasy" was regularly lumped together with science fiction in a way many geeks would today find unpalatable. Such hard distinctions were unknown and likely unwanted.
In this respect, the original sensibilities of D&D share a great deal in common with those of anime. The willingness to accept that "fantasy" means "anything unreal" is something that was commoner in the early days of the hobby than it is now. Oftentimes, when people wish to claim that such-and-such "doesn't belong" in D&D (or even "isn't D&D"), it's said out of a sense that D&D has an internal coherence that only evolved years after it began. This is why I feel OD&D offers an important corrective to lots of misunderstandings about the games that descended from it. It's hard to read OD&D with unbiased eyes and not see that the people who created it and certainly the people who played it had a very different conception of "fantasy" than do many people who play the game today. I won't go so far as to say they had a better one, because that's a wholly subjective judgment. But there's no denying that, in this respect, D&D today is very different than its origins.
By my lights, Dungeons & Dragons used to have more in common with anime than it does now and that's a shame.