All to do with process.... First you face x line with y line so many times until " is that ruy Chavez?" E4 e5 knf3 knc6 Bb5 blah blah blah BxKnc6!!!!!!!
Nagging problems, Part I: I can't remember

You're able to remember it? Eyes as you know full well I am nowhere near as sharp as you. Seriously.
@1
"I either don't know or can't remember what those things are or what they look like."
++ Do not worry about openings or opening names. Worry about avoiding blunders.
"have to pull up a board to look up which square is which"
++ It comes with practice.
It seems to me that the very competent players know as second nature a whole slew of things that I cannot remember. For example, if an experienced player starts talking to me about "mainline" vs. "sideline" or "Caro-Kann Defense" vs. "Slav Defense," I either don't know or can't remember what those things are or what they look like. I have watched vidya and read books covering them but not long after I forget all about them, and many, many others besides these. X Defense as opposed to Y, or Y Modern Variation, and how to counter each, and with what pieces, in what sequence, with what possible variations, are all things I can't remember on a week to week basis, much less in a game.
Another issue is that when an experienced player tells me, "Nd4 is a better mover than Bc3," I literally do not know where that is, and have to pull up a board to look up which square is which and figure out what is going on.
Put another way, I am as slow as molasses in January.
Realistically speaking, how far can an ordinary, non-prodigy player hope to advance if they do not know each and every (or at least most) of these core concepts purely from memory?
All that comes with experience. You only played a couple of games. I didn't know any of those things either when I started playing chess.
It seems to me that the very competent players know as second nature a whole slew of things that I cannot remember. For example, if an experienced player starts talking to me about "mainline" vs. "sideline" or "Caro-Kann Defense" vs. "Slav Defense," I either don't know or can't remember what those things are or what they look like. I have watched vidya and read books covering them but not long after I forget all about them, and many, many others besides these. X Defense as opposed to Y, or Y Modern Variation, and how to counter each, and with what pieces, in what sequence, with what possible variations, are all things I can't remember on a week to week basis, much less in a game.
Another issue is that when an experienced player tells me, "Nd4 is a better mover than Bc3," I literally do not know where that is, and have to pull up a board to look up which square is which and figure out what is going on.
Put another way, I am as slow as molasses in January.
Realistically speaking, how far can an ordinary, non-prodigy player hope to advance if they do not know each and every (or at least most) of these core concepts purely from memory?
This happens when you read too much and play too little. It reminds me of how we started studying programming in highschool. 2 months of theory with no practice. A catastrophy. You will remember these things by playing chess games, reviewing your games and trying to implement what you have learned little by little. If you just study chess like a highschooler studies biology and you don't play a lot then learning all these things will be very difficult and you will view it as a chore as opposed to viewing it as something that you want to do so that you are prepared for the next time you see that position or a similar position.

It seems to me that the very competent players know as second nature a whole slew of things that I cannot remember. For example, if an experienced player starts talking to me about "mainline" vs. "sideline" or "Caro-Kann Defense" vs. "Slav Defense," I either don't know or can't remember what those things are or what they look like. I have watched vidya and read books covering them but not long after I forget all about them, and many, many others besides these. X Defense as opposed to Y, or Y Modern Variation, and how to counter each, and with what pieces, in what sequence, with what possible variations, are all things I can't remember on a week to week basis, much less in a game.
Another issue is that when an experienced player tells me, "Nd4 is a better mover than Bc3," I literally do not know where that is, and have to pull up a board to look up which square is which and figure out what is going on.
Put another way, I am as slow as molasses in January.
Realistically speaking, how far can an ordinary, non-prodigy player hope to advance if they do not know each and every (or at least most) of these core concepts purely from memory?
This happens when you read too much and play too little. If you just study chess like a highschooler studies biology and you don't play a lot then learning all these things will be very difficult and you will view it as a chore as opposed to viewing it as something that you want to do so that you are prepared for the next time you see that position or a similar position.
You raise an interesting point. My understanding was that playing more than reading/studying first wouldn't get me anywhere, because I had not learned tactics, strategy, and many other things. That was what some experienced people said, at least.
"As a general rule of thumb you want to be studying and learning more than playing if you want to improve, especially at the lower rating ranges."
- TheNumberTwenty

I'm getting a little better at listening to people rattle off notation in videos and actually being able to somewhat follow it, but boy do I have a long way to go.
Chess.com does have a pretty cool training tool for learning the squares. Give this a try. Obviously do it as both black and white.

This happens when you read too much and play too little. It reminds me of how we started studying programming in highschool. 2 months of theory with no practice. A catastrophy. You will remember these things by playing chess games, reviewing your games and trying to implement what you have learned little by little. If you just study chess like a highschooler studies biology and you don't play a lot then learning all these things will be very difficult and you will view it as a chore as opposed to viewing it as something that you want to do so that you are prepared for the next time you see that position or a similar position.
I'm a firm believer that more study and less games is the way to go. Longer time controls and a lot of analysis on completed games is what I do but to each their own.
It seems to me that the very competent players know as second nature a whole slew of things that I cannot remember. For example, if an experienced player starts talking to me about "mainline" vs. "sideline" or "Caro-Kann Defense" vs. "Slav Defense," I either don't know or can't remember what those things are or what they look like. I have watched vidya and read books covering them but not long after I forget all about them, and many, many others besides these. X Defense as opposed to Y, or Y Modern Variation, and how to counter each, and with what pieces, in what sequence, with what possible variations, are all things I can't remember on a week to week basis, much less in a game.
Another issue is that when an experienced player tells me, "Nd4 is a better mover than Bc3," I literally do not know where that is, and have to pull up a board to look up which square is which and figure out what is going on.
Put another way, I am as slow as molasses in January.
Realistically speaking, how far can an ordinary, non-prodigy player hope to advance if they do not know each and every (or at least most) of these core concepts purely from memory?