I can kinda make sense of that. Just for myself, I don't see that as going OSR - because those classic D&Ders were bringing a lot of wargaming experience to the table!
That assumes a LOT of facts not in evidence...
(bit of a rant...)
We hear a lot about it in print - because early D&D discussions were largely in wargaming magazines and local fanzines; the latter mostly don't survive. But we also see in Dragon a lot of questions that show that, by 1976, a lot of D&D players were not experienced wargamers. And then there are folks like Liz Danforth, Bear Peters, and Michael Stackpole... who, thanks to Ken St. Andre, started "D&D" with a totally different ruleset, since Ken St. Andre (a wargame designer) disliked the OE rules and rewrote them... largely without reference to wargames mechanics.
Did some come in as experienced wargamers? Oh, hell yes! Me included... but I was introduced to D&D by guys whose only wargames wee Risk, Stratego, and Chess. (unless you count checkers and chinese checkers; but I count those as abstracts, and chess is a painted on theme...) Me? I'd played Avalon Hill's
1776 and
Outdoor Survival, and
Tactics II, plus all of the above "family-game wargames"... but that's also summer of 1981.
And most of the guys I met thereafter playing, even if they started before I did, had no prior wargaming. I'd estimate about 1 in 3 to 1 in 4 had any minis-gaming or counters-on-map gaming experience, tho about 3 in 4 had experience with those 3 "family game" war-themed games... Chess, Risk, and Stratego.
We need to avoid typcasting the 1974-1977 era as "mostly wargamers" because there is a
known preservation bias for the commercial wargaming magazines. We know that the first sales are in wargame conventions... but within the year, a few stories of accidental hobby-shop buys by non-wargamers start. And also recruiting of non-gaming friends into D&D without wargames first also start to show up in the available historical information. And the first variants without intent for wargaming experience (EG: Tunnels and Trolls).
At best, we legitimately can say wargamers were the
intended audience. (Various statements over the years by Gygax, initial sales at wargaming conventions, and my own correspondence with Mr. Arneson.)