This is close but not exactly right, and the small difference matters. Elo does not assume that skill is normally distributed, but rather that "quality of play" in a single game is normally distributed around some average quality level for the player. Obviously this too is an approximation but it's a much smaller one.
I would think player skill level (at best; there easily can be cases where P typically beats Q, Q beats R and R beats P) is an ordinal (https://en.wikipedia.org/wiki/Ordinal_data), so one can’t say “player P is twice as good as player Q”, “player P is as much better than player Q as player R is better than player S”, and certainly can’t prove or disprove whether skill is being normally distributed. It is customary to assume that, though.
Also, if one assigns numbers to skill levels, those can be normally distributed. It probably is possible to design an ELO-like system that, given enough games, guarantees that the set of skill level numbers of all players approaches being normally distributed.
https://2p1ipt36o1g23g1tt6ba5nou-wpengine.netdna-ssl.com/wp-...
This report is nicer than many others I found in that scores are reported all the way down to 0, rather than cutting off at the threshold for university admission. It's much less nice than some in that, below the university admission threshold, scores are reported in brackets of 10 points rather than by individual score. (This, even though the document is called "一分一段表"...)
Anyway, I imported this data into python and plotted it with matplotlib. The histogram you get from this is obviously, wildly flawed -- the ten-points-wide bar from 410 to 419 is also 710 people tall, dwarfing the actual mode of the distribution. To correct this problem, you need to divide the count for bracketed scores by 10 (the width of the bracket) -- the 710 people scoring 410-419 are 71 per score in that range, very comparable to the 70 people scoring 420, but not to the 182 people scoring 548.
Without knowing the width of the rocket league rank brackets, that picture of the population of each rank doesn't tell us anything -- at all -- about the shape of the distribution.
especially with well-established, popular games-- Chess, League of Legends, Overwatch, etc. (where there is even a financial interest in being a top player to boot), the skill levels of the people at the absolute top simply profoundly dwarf players that would even superficially seem "comparable" by the standard of being in adjacent, or even within the same tier.
in League of Legends, for example, it is often claimed that the differences between players in high/low Challenger, high/low Master's, and even high/low "high diamond" (low d2 vs high d1) all constitute distinct "tiers" of player quality that are as substantial as the full-tier jumps closer to the median (e.g. silver -> gold, gold -> platinum), but because of this shoehorned prior about skill distribution it leads to this compression at the very top.