I think firearms might be more prevalent. Gygax didn't want them at all in D&D; I read one of his Dragon Mag editorials which outright said that if you brought in guns, it wasn't AD&D anymore. But in this version, they'd be part of the game from the start. Also, the setting itself would likely be more science fantasy rather than pseudo-Medieval.
Mind you, if D&D were made today, and especially if it wasn't the immediate offspring of wargames, there might be
much less of an emphasis on combat. Combat would still be there, of course, but there would be of a lot less importance.
Disagreeing on this one. Races almost certainly would be different. We're in a post Warcraft and Warhammer world. We'd have humans, elves, dwarves, orcs and goblins. Maybe gnomes. Almost certainly not halflings. Heck, minotaurs have a better chance of getting in as base over halflings. There just isn't the market drive out there for short hobbit-y folks as there used to be and gnome would snap it up quicker
Additionally a lot of the stuff that exists due to D&D's history and how its handled stuff historically wouldn't exist. Almost certainly wouldn't have 'cleric' as the healer, wouldn't be so much baggage on the ranger, and I'm honestly gonna say that sorcerer and wizard would be completely different in pretty much everything about them.
I'd add that we'd probably have more anthro races. Or very alien races--as
@PsyzhranV2 mentioned, space opera might be more prevalent and would leak into fantasy in some way. I could see more plant- or stone/crystal/metal-folk as a result, or more slime-people.
Although I disagree about the halflings--I think they would stay (due to Tolkien, who would presumably still have written his books), and the idea of "humans, but tiny" is pretty universal. They may have been more fey-like than anything, or else
very tiny, like Lilliputians. But mostly I disagree because I've know more than a few people who
really liked short races. I could see gnomes being a magical subrace of dwarf. Mind you,
dwarf might be renamed, should D&D have been made today, perhaps using actual mythical names.
I agree about the cleric/healer thing. I seem to recall that original D&D didn't have any gods, and they might have continued with that. Or they might have decided that D&D-land has an animistic/spirit thing and avoided any sort of deity idea, thus making things like witches and shamen the default divine casters. This might end up reducing or removing the existence of celestials and fiends, and perhaps upped the importance of elementals and fey.
I'm not sure what you mean by the ranger's baggage, other than their lack of focus as a class.
I have to wonder if something akin to a 5e paladin--someone who fights due to an obsessive oath--might be around from the start (but with a different name: Vowkeeper?). There's plenty of non-fantasy cinematic examples of characters like that (Batman, for a very obvious one) to be used as a basis.
Oh, also, it would be vastly less exclusively European than D&D. Like...almost certainly.
I definitely agree there. At the very least, assuming video games and martial arts movies were still as popular in this alternate universe, then Japan and China would be a major influence. As an example, even baseline fighters might be far more wuxia in nature then they are now. And with the internet being so available, it would be much easier to bring in interesting aspects of other cultures and making them part of the core set rather than as add-ons.
I also like to think that this might have reduced the number of creatures that have variants of the same name as a side effect. Drow and duegar both come from the same word in real life; they might have become a single people in this D&D.
That means that the nascent computer-gaming industry didn't produce classics like Zork, and we lost out on a lot of great text-based adventure games.
But sci-fi might have filled in that gap. Zork may have taken place on an alien world or in a damaged spaceship instead. Grues are aliens that live in the darkness of space.