I think that, if one were to do this thought experiment properly, one would need to remove all those things which were were heavily influenced by Dungeons & Dragons.
I would therefore put most medieval Western fantasy literature post-Belgariad (and possibly earlier, though the Belgariad shows fewer D&D influences than the Elenium) out. Following this line of thought, I do not know if Dresden would have been made, but it is possible. Harry Potter is independent of D&D, so it would still exist. Jonathan Strange & Mr. Norrell would still exist, as would any other fairy-inspired story. Pratchett would still exist, as his Discworld started as a parody of the old S&S stories. Alvin Maker would probably still exist.
For video games, while Gauntlet is obviously mappable to D&D, Dragon’s Lair, King’s Quest, and the original The Legend of Zelda are not. Unfortunately, most video games set in fantasy worlds are highly influenced by D&D and its tropes, so it would be much more difficult to find games which work.
For cartoons, every 70s and 80s fantasy cartoon, apart from D&D, would be kept. Your Thundarr, He-Man, Galtar, and Thundercats would have large influences. Dark Water could stay. Avatar would definitely be kept.
For cinema, more is available. Of course, Star Wars would have a major impact. Flash Gordon would be bigger in impact, as would movies like Outlander, The Thirteenth Warrior, Reign of Fire, Willow, Conan (naturally), Hercules, Neverending Story, and so on.
In anime, a good portion of the instantly-recognizable series, including my beloved Lodoss, would never have come to be. However, DBZ, JoJo, One Piece, Fairy Tail, would still have come about, as they pull from different mythical sources. You’d also see influence from various sci-fi properties like Harlock, Voltron, Cowboy Bebop, Space Dandy, and so on. FMA, using an alternate history of sorts with very specific magic, would be good.
So, what would a world like that leave us with?
First, we would likely see a bigger gap between fairy stories and what fantasy would have become.
One the on hand, you would have your fairy tales and medieval romance, where people would continue to take the ideas of the intersection of the mortal and immortal worlds, and how that influences mortal lives. Expect to see more RPGs and video games that have more in common with the sensibilities of Gaiman, and it would be very popular.
On the other hand, you would have the alternate equivalent of fantasy, which would be far more influenced by, and containing more of, sci-fi. There would be more machines, more robots, and more planets. Think of this as more cosmic. It would be, in effect, more science fantasy, though wider, deeper, and more varied than in our world.
Well, a good number of these properties have a preponderance of fighting types, whether mundane or with some supernatural elements. Give the relative lack of organized military in the vein of Napoleonic or before armies, the divisions amongst various fighter types would be far less on what type of unit they fought with, and more with where they fell in the mundane-mystical spectrum. In other words, our understanding of classes would be right out, as that’s derived from wargaming.
Magic is typically soft, with the idea of casting a spell just being the act of using magic, and the effect depending upon desire; actual hard magic would be rare. There would likely be something similar to 4e/5e’s ritual magic, as you will often find in the influences mentioned above the need for the big wizard or sorcerer to have to use a ritual that can take days to cast.
You’d see more characters with some level of magic, even if it’s just a knack that’s highly specific.
I will reiterate that I believe that, without D&D being created the way that it was, there would be no classes. I also do not believe that there would as big a mundane/mystical divide.
What we now
Now, the most unpopular part of this thought experiment? I do not believe, given the sources which would still have been made in this alternate timeline, that there would have been any standard races but human. Each game system or campaign setting would include its own various races and species, and many of these would be aliens.
So, what would this new world of D&D look like? Classless, skill-based, with far more varied and present magic, weird aliens, strange technology, and big epic stories. Heck, it probably would be something like Exalted or other WoD games, as far as builds.
it’s interesting how this world would have turned out. D&D has had an outsized influence on the development of Western fantasy, and how we view it. Without it, I seriously doubt that fairy tales and medieval romance would have merged so strongly with weird fiction and sci-fi, and thereby creating a good bit of the cognitive dissonance that D&D fans have experienced over the last five decades.