I coined using the term "adventure game" for roleplaying games in February 2012, and I've been using it since then consistently instead of "roleplaying game". There's been a recent discussion around the term started by Ben Milton, so I thought I might as well explain why I started using it in the first place.
I've summarised bits and pieces of my philosophy before on my blog. One doesn't have to read all of these, but they show variations and developments in my thought over the past seven years.
The Long Narrative
Roleplaying: Beyond Talking
The Basis of the Game Is Making Decisions
Running Technical Plots
Layers of the Sandbox
Low Concept Campaigns
I would say I first began thinking along these lines in 2008, when 4th edition Dungeons and Dragons came out and there was a sprawling online kerfuffle over "dissociated mechanics" at the same time as a concept known as "bleed" began to sweep LARPing circles. There was also a lot of debate around how "collaborative world building" and "collaborative storytelling" could be used to help referees give up the idea that they were writing an epic fantasy novel with the players as the railroaded protagonists. I don't know how successful this actually was (I still see questions regularly on Reddit about how to get the players to follow the amazing story the referee has come up with), but it was the context around when I began to think about what I used to call "anti-narrativism".
Anyhow, the four years from 2008-2012 not only had me reading a lot about these controversies, but it also saw the end of my then-regular gaming group (in late 2009, when the referee moved out of town) and my first foray into OSR-style games (Swords and Wizardry Complete, in particular). I engaged in a process of reflection about what I was trying to do with and in "roleplaying games" as I still mostly referred to them at the time.
The answer to what I concluded isn't simple or easy to sum up, but one element was that I realised that my prior conception of "roleplaying games" was not that different from the "immersion" crowd, and while not wrong, it was simply insufficiently broad to encompass all the things I liked about games, and also, from the perspective of producing enjoyable games, it misled me about how to do that by encouraging an emphasis on dramatic elements like acting out characters and vividly narrating a story.
Instead of skill of the portrayal of the character, it was the agency (and on the level of the party and group, the deliberation that fed into that agency) that I particularly prized as a player, and that I realised formed a set of key skills that players needed to develop even before they built up their acting chops.
To provide the stable and intelligible foundation for the shared world the player-characters move through, I needed to structure the decisions and consequences of those decisions, and to constantly communicate them clearly back to the players.
A player might talk in the third-person about their character or not, they might use a funny voice or not, their character might not have any family or background or whatever, but if we could make the choices that character made interesting and evocative and varied and relevant, the rest fell into place.
I chose "adventure game" to represent that refocusing (I also chose to begin referring to the "dungeon master" or "games master" as a "referee" most of the time). For me, the core of gameplay is not narrative (not a series of rising actions that develop to a climax and then resolve in a denouement), but iterative, and the things being iterated and reiterated are procedures, little list of instructions that govern how and when to apply or not apply the various rules.
The classic example in most adventure games is the combat procedure, which tells you how to set up combat encounters, determine in what order players proceed, how and what they can do, and then delivers some set of consequences based on their decisions and various randomising factors. Once you complete a loop of this procedure, you reiterate it for the next combat round until some end condition is met.
My preference is to be continuously enacting one procedure or another, or when not possible, to provide a set of structured steps that lead the players through deliberations with one another that resolve into decisions they make and consequences they bear for them. Oddly, this often ends up resembling a traditional story (and I have no objection to its mere appearance as such), but I treasure the times where it doesn't in particular, as these are the moments where the adventure game medium generates something new and unexpected.
The "adventure" then is not the narrative the player-characters flow through towards an inevitable climax and resolution, but the procession of problems, challenges, etc. they face; the decisions and deliberations they make about what to do about each problem or challenge; and the procedures they enact as part of those decisions, and the consequences of all the above interacting with one another.
Many people have been calling this sort of playstyle "OSR-style", though that to me associates it too closely with a particular subset of games (mostly rules-light D&D variants) and subculture of product design, and loses the idea that it is a playstyle that can be applied to almost any "roleplaying game" (Some with more easily than others, admittedly).
Recently, as people have begun wanting to move away from calling themselves "OSR" for political reasons and to characterise their playstyle using a different term, I've repeatedly suggested "adventure games" as an alternative. I think of the OSR as a particular subculture, with a particular attitude towards independent publishing, the history of gaming, etc., but I think the playstyle characterised by "adventure games" is one that is not specific to it, and that this playstyle should be developed and shared more widely so that even people who are not part of that subculture can learn it and adopt whatever practices from it they find most useful, in the same way people think of "storygaming" or "trad roleplaying games" as distinct playstyles to be developed and studied.
In that sense, I don't see "adventure game" as a replacement for the "OSR" concept itself (referring to the subculture), but only for the "OSR-style" or "OSR playstyle" terms. And obviously, I encourage you to use it as such.