Basic D&D was written by Moldvay, Metzner, and Cook. AD&D by Gygax alone. David Cook wrote 2e. 3e was by Williams, Monte Cook, and Tweet. 4e by Collins and Wyatt, and 5e by Wyatt, Schwalb and Cordell. None of them are, technically, "the game that Gyga and Arneson" wrote. Are they not D&D?
There seems to be some weird thing going on here with people's readings of necessary vs sufficient conditions.
A sufficient condition for someone playing D&D is that they are playing the game that Gygax and Arneson wrote. So any account of playing D&D that excludes that (eg because it excludes making stuff up, or dropping stuff into your world from some other world - like the way Blackmoor is dropped into GH) is too narrow.
That doesn't mean that playing OD&D is a necessary condition for playing D&D. And in general I don't think it's helpful to try and stipulate, in advance of any particular instance of play being described, what would be the necessary conditions of playing D&D. Because, like any cultural/creative activity, there's always the possibility, even likelihood, that someone will come up with a new and unanticipated way to do it.
Further, does running Star Wars d20 count?
I'll only respond to one of these questions, because my answer generalises fairly straightforwardly.
By default, probably not, because someone playing Star Wars d20 is deliberately eschewing D&D. It's a different genre and a distinctive setting. (Much the same as CoC is not RQ, even though the core mechanics are the same.)
But it's pretty easy to imagine departures from the default. For instance, there must be plenty of tables out there that used the d20 Star Wars rules to put Jedi PCs into their D&D games. Those tables are playing D&D, just as Murlynd is a D&D character who happened to travel to Boot Hill and pick up some six-shooters.
if I change how cantrips work in my game, I don't say I'm still following the Core Rulebooks as written. Likewise, if I change where blue dragons live or the alignment of gnolls, I can't say I'm following the Core Rulebooks as written either.
But who do you think this is contradicting?
The thing is, if you change cantrips to be X/day rather than at-will, that doesn't mean you're not playing 5e D&D.
I never said that I'm playing strictly canonical GH. Which is to say that I didn't lie. I said I'm playing a GH game.