I think my list would look a little different than most. I'm not sure if it's possible to rank everything, but I think there are a few related things that are important.
Disclaimer: I don't have enough time to dedicated to be a high-level competitive player myself, but these are things I've learned from observing other people.
FUNDAMENTALS
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1) How Does This Game Work?
So the meta of the game. In Moral Kombat for example, we'd be talking about when to poke, when to block, how blockstun and hitstun work, how strings work and how to defend against in-baked mixups, etc. What are the different strings designed to do? The specials? What does the designer probably intend certain things to be used for? This kind of study tells you what your options are.
2) How Do Fighting Games Work?
So over time, there are a lot of different archetypes for characters and tools that people have had to deal with. Things like footsies, spacing, etc. are universal. Dealing with jumping or dashing, how do deal with advancing specials and mids, getting in on zoning, etc. are things that have common traits between a lot of games.
No matter how well you know your own game, it's hard to win competitively without this stuff. And sometimes people can get by with fundamentals when their knowledge fails them.
STRATEGY
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3) Solutions to Problems
So this is a huge area that sets levels of players apart. And that is: once we're all playing with the same tools, how do you solve the problems that you face?
Problems could be:
-I'm having trouble getting in range because of the range on my opponent's normals, or he projectiles they're throwing
-I need to get out of the corner
-I need to deal with a string that my opponent can end different ways
-I need to deal with the staggers that are being used against me
-I'm getting hit with this after my opponent does this
-I'm getting thrown a lot in in this situation
Each good player is going to play to the strengths that their character utilizes best -- and your job is to figure out answers to the problems that those playstyles pose. One thing that separates great players from great is their habit of being able to find solutions, vs. just continuing to do the same things.
*How do you learn solutions to problems? If you're not lucky enough to have someone tell you (like a great training partner), then looking at what great players are doing in the thousands of matches out there is a wonderful start. If you're having a problem with something Geras is doing, how did Dragon deal with it? How did some other top player deal with it? Or just someone who plays a matchup well. Etc.
Also looking at what other people are doing to you is a great way to learn. When you can learn from the tactics good opponents are using on you in real time, you're on your way to improvement.
3.5) Flexibility -- Just a minor point; you can't actively choose the best solutions to your problems if you're unable to be flexible with what you do in a given situation. So in order to allow yourself to actually use better solutions in realtime, you have to work on being flexible. It's hard to be a great player when there's no variation in your play, and being locked into habits and patters is something that separates midlevel players form the better ones.
4) How Do Other People Play
So aside from #3, the biggest thing that separates players is their understanding of what their opponents are likely to do. Everyone always talks about reactions, but the fastest reactions always happen when you already expect what you're reacting to.
The mark of a great player is being able to expect what their opponent will do next, and being able to plan for that in advance. So no matter how much you know about your game, knowing the tendencies of what human beings will do is what allows you to beat other human beings. Knowing when they're trying to bait you, condition you, etc.
This means you need to get good at:
-Seeing patterns. Does this person generally wake up a certain way? Do they general do one thing after another thing? How does this person move in neutral?
-Just knowing human tendencies. When do people tend to jump? When do they block, duck, attack, roll, poke, etc.? What do people do when faced with certain situations? When they're cornered, when they're down majorly on life?
-Manipulating people. How do I get this person to do what I want them to do? How do I condition them to expect something different than what I'm actually going to do?
This ranges from the bigger stuff, which we generally call "Yomi" (which is basically being able to turn whatever you opponent wants to do next into a disadvantage for them, and an advantage for you), to the small things. You need to know what you opponent expects you to do, do you can hit them with something else.
Micro-timing, for example, is something small that has big repercussions. When you watch great players play, they will often take a split second and hesitate in certain situations, rather than just committing right away, to see if their opponent will try something. Minor hesitations, tiny walkbacks, being able to interrupt someone in the middle of what they're trying to do rather than trying before or after it, all make big differences competitively.
SELF MANAGEMENT
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So aside from knowing your game and knowing how other people play, the last truly important category is knowing how to manage yourself most effectively. That includes stuff like:
5) Self-Honesty
Being able to admit when you screwed something up. When you're doing something wrong. Being able to look back critically at your own play and find the holes in it. To admit when you're not playing as well as you could have. If you don't know matchups, then you work on it to fill those gaps. If you're struggling against zoning, then you work on it until that hole is filled. If you need to play someone to work on an aspect of the game, you go get them and grind it out until you're better.
To be great you should learn from any and every loss, no exceptions. Being able to ask "What should I have done better?" is probably the most important skill in fighting games.
6) Emotional Management
If you want to compete, you've got to be able to manage your emotions as well. Being able to stay calm when something bad happens in the match.. Keeping your head about you and not freaking out late in the game.. Being able to mentally calm yourself when you're down 0-2 and rationally work through adjustments to make a comeback. Being able to shake off a bad set in order to come back and win something in losers. Being able to hang in there when you have a bad couple weeks and you're losing to everybody. Being able to stay calm when you're winning massively to avoid becoming cocky and making a mistake that costs you. Etc.
Being able to tune out your own self-doubts in critical moments. Being able to stop you from defeating your own self. Dealing with pressure. Dealing with distractions, crowds, noise.
Have the attitude to learn from every loss in your casual sets, instead of just being depressed about it, or complaining that it's unfair. Even if you have a low moment, being able to come back the next day and figure it out rather than just crying and losing.
6) Practice
It goes without saying, but what you'll only do you know you should do in the moment, if you make a habit out of doing it. If it's not a habit, that moment will come and go before you have a chance.
Building habits takes repetition. Lots of it. The reason I list this after everything else above is that it's not just the time -- you need to build good habits, which takes the discipline of knowing what you're supposed to do. But extended practice is what makes your instincts sharp enough to be able to do it. You can include execution and things like that in this category.
7) Preparedness
This comes from practice, but I think it's also a general habit on a personal level. The guys that watch tape on everybody else before a tournament.. Scout their opponents and find their strengths.. Just generally being aware of what you could be faced with competitively and already being ready for it when it hits you. These are the people who get the edge when it's tournament time. Just getting in the mindset of being as prepared as possible before you walk into any situation. "What do I need to do to be ready for this event?" "What do I need to do to be ready for this player?" It's an important life skill that can get you ahead in many areas.
The best players I know have all spent time preparing for specific situations they'd run into in tournaments, preparing for Top 8 the next day, etc. It's a lifestyle.