Identical twins still have different names. That said, the all-guys-are-Steve piece is a red herring here.Because it's like calling every guy Steve just because they share some basic physical similarities. John is Steve, Tim is Steve, Joe is Steve, etc. It would be confusing and nonsensical.
D&D is the stuff that says D&D on the cover. Other works may be D&D derived (True 20, Level Up) or D&D inspired (Conan 2d20, Monsterpunk) but they clearly aren't D&D anymore than John or Tim are named Steve.
There's D&D - which within itself has a pretty wide variety of stuff included if we look at all the editions put together - and then there's a bunch of other 'adjacent' games and a slew of kitbashed and homebrew systems that used D&D (whatever edition) as the launching point. They're all close enough for rock'n'roll, so just call 'em d&d with small 'd's.
I see the war-v-sport discussion as a) applicable to much more than just combat and b) as edition-agnostic and almost system-agnostic; pretty much any d&d-like system can be run either way, depending what the DM and-or players want to do with it.
That said, some systems and-or editions clearly trend toward one or the other as their default, which serves to turn these discussions into proxy edition wars, which defeats the purpose of having the discussion inthe first place..