game ratings: I smell a rat!

Does anyone know how the game rating system works? I originally assumed it looked at the actual moves made in the game, and estimated how well the players had played based on those moves alone.

But I'm smelling a giant rat! I was getting a slightly rat-like odour already, as a player who tends to yo-yo up and down the scale. I notice that when I'm down in the 300's, even if I play as well as I can, my game ratings are pretty low, probably not above 900. But as soon as I get up to 550, I can reach 1300 on occasional games. But I'm still playing the same.

I just looked at a game between two players rated over 2000. It's the same 10-minute time control as I use. The game is a right shocker! It's full of obvious blunders, both players failing simple issues of counting, both blundering away pieces for nothing I thought maybe I was missing subtle issues of position: maybe they didn't pursue a series of takes and take-backs that leaves them a bishop ahead because it was going to cause some other catastrophe. But Stockfish agrees with me, not them; stockfish awards both players a long list of mistakes and misses, and a blunder each. The final accuracies were 66.8 and 71.2, and yet the game ratings of the players were 1600 and 1650.

I'm wondering whether the game rating system actually takes the players' ratings into consideration, and gives an increment or decrement from the player rating depending on the overall quality of the chess? Or maybe, if it's some AI thing, it's biased by the quality of players who typically find themselves in a particular position? (i.e. it's using the players' ratings indirectly: if there is an opening that is typically played by 400-level players, then most data on the best response will be from 400-level players, so even if the move you choose is exactly the one that a 2000-player would make -  if they were playing the game - the model will rate you as 400 because most players who made that move are 400, so that's the rating that is typical of that move???).

The post game review ratings are estimates based on the ratings of the players and the accuracies.

If you take a game and change the ratings the estimates will also change

Your understanding is not correct. Ratings are not based on an assessment of the quality of your play. They are based on whether you win, lose or draw and the difference between your rating and your opponent's. There is also a component which judges how accurate your rating is likely to be, based on how many recent games you have played.

https://support.chess.com/en/articles/8566476-how-do-ratings-work-on-chess-com

If two GMs intentionally play as badly as possible, it will still give both of them a 2000+ rating. Don't take it seriously.

After a win it tells you that you are around 300 Points better than your rating, to keep you playing (consuming the product). After a loss it tells you that you are around 300 points below your rating, to keep you hooked for improvement (consuming the product)