I break the tiers down into 3 categories.
1) Literacy. Can you move and shoot in the FPS? Know how pieces move in chess? Basics of the how to play. You must master these and make them reflexive to move forward.
2) Fundamentals. The emergent gameplay that arises from those basic rules. But importantly these are all contained within the game. I usually break these up into Tactics and Strategy. Tactics are the moment-to-moment events. Strategy are longer-term goals that help guide you towards victory, and understanding how overlapping or even conflicting strategies can work in synergy and in trade-offs.
For example, in chess tactics are things like recognizing forks and skewers. Strategy involves "controlling the center" or "develop your pieces to good squares."
In MOBAs, last hitting, skill combos, space control are the tactics. Strategy can involve knowing when to push, when to group to gank vs split push, or farm vs gank decisions.
Interestingly some game types have more tactics/strategy components. Twitch FPS games tend to be almost all tactics with a bit of strategy (gun X better in situation Y). Starcraft rewards strategy more heavily (do better macro!).
These are, as you mention, skills that will apply to the vast majority of games because they are baked into the rules of the game.
3) The Meta. Once you are near the Fundamentals skill cap, you can use information outside of the game to get an edge against similar opponents. I'm about to play player X, and they usually like to do Y, so I should prepare a counter strategy Z. A lot of players seem to really like character A because of these advantages, perhaps I should learn A and how to counter the most common tactics using my character's skillset.
Note knowing the Meta also helps prune what information (Fundamentals) you need to learn and maintain. If no one plays character Foo, then you (probably) don't need to understand their kit as intimately. But then someone could use it as an off-meta pick to surprise you! So you should be at least familiar enough to refute it just in case.