Largely irrelevant...
Unprovable. RPG-like minis gaming was on the rise in many groups; if it hadn't been Arneson and Gygax, it could have wound up arising out Tolkienizing any 1:figure:soldier wargame. Or from the warped minds of Cali, better known as The Chaosium, as they were looking for a way to better explore Stafford's Glorantha (which originates in a late 60's wargame). Or from the SCA, which, while not a LARP, per se (no character sheets, no competency simulation mechanics), definitely spawned a couple LARP-like spinoffs in the 70's... It only takes a short wargaming hop for a LARPer to reinvent TTRPG.
A number of character per token games were in development - and came out in the early 70's. Most important to D&D is AH's Outdoor Survival. Add a GM and relax the restrictions, and it's an RPG.
The thing is, RPGs can spin off from any number of sources... it's a matter of just that Gygax had the connections and Arneson the ability to explain it to Gygax... (Too bad he didn't shop it to Flying Buffalo or SPI...)
Original D&D was a bad job editing and layout for the time; if you don't believe me, check out any of the 1965-1972 games from Avalon Hill, or 3M, or SPI, Or even the layout and editing of Strategic Review, by TSR themselves. Or Chainmail. Chainmail is FAR better written than the core. Or the Dahlun Manuscript, for that matter.
RPG's could have arisen from the nascent LARP scene (which isn't really tied to D&D, since LARPing really starts after the SCA becomes two kingdoms and has disaffected former members... late 1960's... and some wanted to gamify it all.
Likewise, ROTC brought minis gaming to many state colleges. This, technically, is how it got to Arneson.
Kriegspiel, especially Frei Kriegspiel, was common on many US university campuses, due to exposure within NROTC.
All it takes is 1:1 wargames, which outside campuses were also starting to get some play time, and you just need to combine either Model UN or Model Senate, or either of the 1960's games, Mr President with Frei Kriegspiel to have simulationist character roleplay.... You need the FK for the "not covered by rules" freedom, especially for underhanded tactics. Or, with Outdoor Surival.
Coulda. Woulda. Shoulda.
If things had been different, they woulda been different. Since they weren’t, they aren’t.
Unless and until we get our own Marvel Multiverse, I will concentrate on the provably true, as opposed to the road not traveled.