I have something to add to this one:
Army Eye, chess as a sport is a competition, indeed. However, there are many people who do not view it as a sport at all, but rather as an art I guess, they just don't care about the sporting aspect of it. Some of them can reach quite an incredible strength because they spend thousands of hours just analyzing, marveling at opportunities/patterns/etc. chess provides. However, they never transmit it to chess competitions (emphasis here), either because they don't care, or they cannot make themselves to(more on that later). So, if you look at it from purely chess is a sport perspective, you would call these people lesser players, however, their actual chess knowledge/skill or whatever you wanna call it is actually very high. So, how to define then them?
I actually have a real life example very close to me.
My main coach when I was a teenager/young adult was only ~2350 ELO (however, he reached this ELO back in Soviet times and then barely played ever again, so in current day it would probably be an equivalent of something around 2500). He was also a long-time coach of a female player who was (and is, though she does not play anymore) firmly in the World Top-10, brought her from nothing basically, as well as some other very strong players, world youth/junior champs and such.
He was (probably still is) an absolute chess fanatic. I don't mean it in a bad way, he just loved it so much that he could spend just unimaginable number of hours looking at anything he could get his hands on. I've conversed with many a GM in my life (no one from the super elite, though), yet never encountered anyone with better profound understanding of chess than him. The thing is, though - he just did not like/want to compete, like at all.
Back in the day, computers were much weaker and therefore the human element was still very important in correspondence chess. He reached some individual success there, but still didn't enjoy it, because he felt competing takes away from his ability to get pleasure out of it. Same with over the board chess - he just didn't like the competition aspect of it and сouldn't live with the fact that he has to constantly make moves that he knows are mistakes/inferior due to time constraints. He liked to compete through his students, if that makes sense, that was all the sense of competition he needed.
So, how to rate this guy? The above mentioned World's top 10 female player, many of her oppnents, Shirov, Peter-Heine Nielsen (main second of Anand in his Wch runs as well as currently main second of Carlsen) have said that his chess understanding is at an incredible level. As a matter of fact, some of his ideas/advice in concrete lines has reached Magnus himself through Nielsen.
And yet, he is clearly a rather weak OTB player and would probably shed a lot of his ~2350 ELO should he start playing again.
So, how to rate him? Everything is not so clear cut