The gauntlet of definitions is ever changing, and it is an important one. Control of the dictionary is was a large portion of online debates are about, even if it doesn’t say so on the surface. In the OSR sphere and post-OSR sphere (BroSR, CAG, etc), there is an important definition debate quietly raging behind the scenes, that over what D&D is.
One contingent argues that the D&D is a war game. The arguments for such can be seen in posts such as this one from Captain Hook. Cutting through the usual bro bluster and rhetoric, we see that there are two arguments actually being made.
Modern war games are actually board games
D&D is actually a war game.
This arguments are drawn from the following assumption: Wargames contain both a Strategic Game, and a Tactical Game. These portions intersect and influence each other. Therefore games like 40k which reset between play sessions (and therefore are only tactical) are not war games. D&D, however, has persistent player characters (alongside troops and other logistic units) and winning or losing a session has real, tangible results for future sessions. This makes D&D a war game.
The obvious hole in this argument is that many modern war games have rules for campaigning. Even lowly Gaslands has rules for running an escalating season that will have strategic results. Running a war game in this manner is a real way to play, but there have always been distinctions between running single battles and running campaigns. The word campaign is as old as the hobby itself and exists explicitly to define this type of play. D&D is distinct from war games in that the campaign is the default way to play. We have to have special words for when we aren’t doing that (one-shot). Compare that to other war games, where someone saying “Come to my place, we are going to play some Napoleonic” could mean a full on 1813 campaign, or just a single battle. You would need clarification. The definitions used in the “D&D is a war game” line of thinking are sloppy. They allow for sloppy conclusions like Warhammer isn’t a war game, but Bloodbowl is (Bloodbowl has a strategic layer after all).
Needless to say, I do not agree that d&d is a wargame at all. Though it descended from wargaming, it has become something different. The best distillation that D&D is not merely a war-game is in this two part post by Diogenes (here, and here).1
But this does beg an important question, namely if D&D is not a war game, then what is it? That’s what I am going to attempt to answer. Importantly, I am going to do so without the use of the term “Role Playing Game” (although this is the actual answer). The reason I want to avoid this definition is that it is bloated and overwrought with meanings. The easiest version of the definition is that D&D is a Heroic Life Simulation game. What the rules of D&D set out to do is create a framework by which the players can experience and participate in a world (the milieu) as heroes of renown (and here I am using the Greek definition of heroic i.e. mighty in deed and action, not the modern definition which implies moral goodness). The way in which it seeks to accomplish this is by empowering one player (the Dungeon Master) to create and play as the entire world which the other players seek to overcome and make their mark own. This is all over the language of AD&D, which references the very fiction it is trying to emulate by way of Appendix N. The characters of Appendix N stories are special, above the normal background characters, and do things outside of that. Including participating in war.
In fact as part of this effort to simulate the heroic life, D&D subsumed many aspects of war gaming. It subsumed mass combat, logistics, fortification construction and many other elements that would have been familiar elements of other war games. But, crucially, D&D is not just those pieces, and those pieces exist to serve the overall goal of simulating a group of heroic characters lives. After all, most heroes become leaders or drivers of men in their careers, so that has to exist or the simulation would be flawed. In the same way that baseball is not merely a batting game, D&D is not merely a war game. Approaching it that way is flawed and leads to flawed games which look nothing like the campaigns actually described in the books. In the same way that Wizards of the Coasts have created a warped and flawed game by focusing only on the narrative part of D&D instead of the whole game.
To illustrate my point, let’s have two scenarios with the same premise. You have been playing a campaign and have gathered an army on the even of a great battle, and then realize that the odds are against you. Do you fight anyway, or make your army retreat, or slink off before you can be defeated and killed? In a campaign driven wargame, say Mordhiem, you may only play out the first option. “Yeah okay there Bob, we know Steve has been steamrolling this league, but it’s your night to play him so just get it over with.” Not playing would be a serious breach of contract in a Mordheim campaign. But in D&D this isn’t as clear cut. All of those options are valid and could make for a good campaign continuation. If you retreat, maybe you get caught by your foe and have to make a daring back foot stand. If you abandon your troops, now you are alone with a host of demoralized and unpayed troops roaming around the country side as bandits, and now you are back to a single actor full of shame. Maybe one of your party members steps up in your place and you have inter-party conflict over your cravenness. All valid outcomes that do not rely on the mass battle at all, and only some from other players. There doesn’t need to be another player controlling the foe’s army because the foe’s army is a piece of the world which you are interacting with, in a myriad of possible ways beyond simple combat.
This is ultimately the heart of D&D. The ability to do and affect the world as a single person, perhaps with a few stalwart allies of renown all their own. It is not merely a backdrop to push units around, the pushing of units stems FROM the actions of the individual. It is the Great Man Theory of gaming. The idea the exploits of one or a few individuals shake the world to its core and beyond.
Footnotes:
OD&D was the closest to war games D&D ever was, to the point that it was sold as a war game. However, it quickly became apparent to Gygax et all that the play patterns of OD&D did not match war gaming, so they came up with the term “Role Playing Game.”


Huh. Interesting. I had not realized this was even a debate.
Although the subtitle of D&D was originally "Rules for Fantastic Medieval Wargames," I have serious doubts that the authors EVER considered the thing "a wargame." This is particularly clear from reading the Foreward to OD&D's Book I, "Men & Magic." Rather, I believe that the subtitle refers to the fact that these are RULES FOR fantastic medieval wargames...a supplementary text/system to such games...and while they may have felt that no one in their right mind would play D&D withOUT the wargaming bits, it is EXPLICIT in Gygax's Foreword that they were aware the game held large appeal even to non-wargamers.
Regardless, Captain Hook's premise is a false one. Yes, D&D offers tactical gameplay...like a wargame. Yes, it offers strategic ("campaign") gameplay...like a wargame. But a wargame holds an endpoint in mind...WINNING THE WAR...and D&D offers no such objective. Despite use of the term "campaign" to describe a particular Dungeon Master's table and on-going game, there is no ultimate enemy to be overcome (via tactics or strategy). Certainly the players will never defeat the Dungeon Master, no matter how hard they try. Yes, they might drive the Dungeon Master from the field (forcing them to abandon the game) but this is not "winning" nor is it a stated objective or victory condition of the game.
Wargamers like Captain Hook may be confused by the wargaming authors' lazy use of terms in describing their own game, but I give Gygax & Co. a break: they created a new type of gaming and they were groping in the dark for a suitable lexicon (calling it a "Braunstein" would have just confused the issue further). However, we now have the term "RPG" to describe the game, as good a term as any...or, at least, it WAS before the term was co-opted to describe the improvisational play-acting that is the prevalent game culture of our present day.