I don't quite agree with that. Why should a newbie, let's say, catch up to someone who has been playing for 3 years in half a year? This is impossible.
And if it is possible, then, let's say, a player has played a sufficient number of games, put in the effort, and then a fresh player comes along and somehow overtakes the other player in a week.
In my opinion, this is not entirely correct.

Added after 19 hours and 3 minutes
After thinking about the rating calculation system, I decided to use the following method:
Rnew=2*(Ga\P + (N+(Gw-Gl)) + 2\3Rold)
Ga - the number of players; P - the place occupied by the player; N = the number of games played; Gw - the number of won games; Gl - the number of lost games; R - rating.
It seems that everything is taken into account here.
Please, criticize)
Sincerely