One of the factors involved in the Old School Renaissance (which is now pretty naissanced, to coin a phrase) has always been quite a bit of argumentation about who's "in it" and who's "out of it." At the very beginning, Rob Kuntz emphatically rejected the idea that he was in an OSR, since he'd been playing old school all along. Many people got very dogmatic about a certain set of "tests," and different "tests" were a popular topic for quite a while. Rob saw the proliferation of "tests" as being the manifesto of a "movement," and since he considered himself not to be part of a movement with exclusions, he opposed the entire idea.
That may have been a correct read on that particular phase of the OSR, actually. It hit a dogmatic patch early in its self-definition, which is also the reason, I think, that RPGPundit also rebelled against the idea that the OSR had any particular value. This despite the fact that his own opinions dovetailed fairly closely with what most of the OSR people were saying.
Anyway, I'm not going to even try, in this article, to propose any kind of overarching definition of the OSR, especially since it still has a variety of different expressions. However, I'd like to mention a very incisive comment by a poster named Wheggi. His comment was that old-school gaming isn't defined by any particular set of attributes: it's more like a syndrome, where if enough factors from a larger set are present in a game, it can be called old-school for lack, frankly, of a better term.
I'll propose a few of these factors, but what's interesting is that some are purely historical, and others evince a system approach that stands outside of its historical context. I tend to think in terms of that ahistorical system approach as being old school, although I also have personal preferences in favor of lots of the other factors -- I just wouldn't consider those other factors to define borders on the definition. I also think that some or many of the historical-context factors can serve to make a game more old school than another, without necessarily making it better or worse.
My own, overarching view of what old-school means is that the rules are open-ended, meaning that the players aren't constrained to particular actions on a character sheet, and that there is a great deal of interpretation, or refereeing, required on the part of the DM. This generally means that "rules-light" is a factor, but not necessarily. You can have an extensive set of rules that don't constrain the DM, they simply define player options. D&D 5e is thus in my mind considerably more old school than D&D 4e, and even 3e. As a rule-set, anyway.
However, here are a few other factors, and REMEMBER I'm not saying ANY of them are independently a defining feature of old-school gaming. Most people will react to several elements with "that's not old school at all," which is my point. The thing is that all those people who reject particular elements ... will pick a DIFFERENT combinations of elements to criticize. Which makes all of them relevant, and none of them dispositive. Also, just because I say something is ahistorical doesn't mean that it's not also part of the historical context, it just means that it can be seen as an old-school principle that isn't purely lodged in time.
- The open-ended, few-rules-on-DM approach I just mentioned (purely outside historical context, it's a game-design and play-method principle)
- Actual rules from the old days, not a retroclone or a later-produced edition (part non-historical, mostly historical context)
- Black & white art, the printing methods used in the early time period (this I consider only to be partly historical, since it's actually something else as well, not just the way books looked in the early days of D&D, but also the way they looked during the Medieval period being presented).
- Blue maps on graph paper (okay, that's purely based on historical context)
- Maps are very much diagrams, with few artistic elements (partly historical-context, but also a non-historical preference for having maps that are easily read during play)
- Gygaxian prose. (Mainly historical, but as a writing style it does have some independent, non-historical effect in terms of flavorful reading)
- Using retro-clones in preference to newer games, even if you don't use actual original rulebooks. (In many cases this is due to the fact that retro-clones have a large audience, available and often-free pdfs, and new products coming out, so it's more of a community and convenience issue than a game-method -- I guess that's non-historical).
- Killer DMing style. This sucks, and is one of the potential failures of an open-ended gaming style, not a defining attribute.
- Letting the dice fall where they may. This is different from aggressive killer-DMing, and I think it fits in as a characteristic of old-school gaming as long as you realize that many, many old-school DMs don't necessarily stick to this approach all the time. Frank Mentzer is, I think, one of the group that focuses on player skill as an offset to the game's purely random element. On the other hand, I think the "dice fall where they may" is an outgrowth of the wargaming roots of the game. It's also a definable, non-historical style of play. So I'll include it as a non-historical element of old school gaming, and a good example of how not every element here is required to push a game into the "old-school" category.
- Weapons and armor remain within historical boundaries, not reaching anime proportions. (I think that's actually a non-historical element, although it's mostly aesthetic)
- Rocks fall, everyone dies. (Non-historical, this is simply a gaming method that takes common sense into account rather than using dice in silly situations. However, filling your adventure with this sort of lethal-but-common-sense trap approach can still fall into the killer-DM category, which is poor adventure design)
- Zero to Hero. This is non-historical, having to do with the strength of starting characters relative to regular people. Many people in the oldest days would still start the characters at higher level than first. It provides, though, a human scale to the heroes, making the game grittier even when the game is at higher level, so it's a definite contrast to newer approaches in which the characters have a sort of super-human feel.
- Sandbox, not railroad. This is both historical and non-historical. It's clearly a matter of design and play-style, which is independent of historical context. However, it's very much connected to the fact that during the 2e period a series of highly railroady adventures were published by TSR, and that most post-2e published adventures are also far more railroaded than what was common in the pre-2e era. This is one of the areas where 1e and 2e people tend to squabble about what's "old school."
- Whatever edition you started with is old school. Very common psychology, obviously not actually relevant in any objective sense.
- No diplomacy checks or other die rolls that can substitute for role-playing that sort of encounter. This is ahistorical, and I think it's a fairly major element.
- Level tends to be more important than character attributes. This is ahistorical in the sense that it is clearly an attribute of the game's design rather than the way in which it's played. It's also probably the one feature of old-school that absolutely doesn't map onto other games than D&D, and doesn't even map onto other games existing in the late 70s.