I am confused about the rating system. I lost a game against a player who was not rated before. He jumped from 1200 to 1660 points after his first rated match, I went down from 1670 to about 1650. I won the next match against the same player, but this game was not rated for me, only for him, although the table says the game had been rated. ????
The first part: rating adjustments for players in the same game can be greatly different because the Glicko rating system used here includes a frequency-of-play factor, RD. A player who has played very few games or very few games lately will have much greater adjustments than one that has played a lot or more frequently recently. See this link regarding ratings.
The 2nd part: a game is rated for both players or unrated for both players. There is no other option. You will have to examine what actually happened more closely. It's possible you are looking at different time control ratings (e.g., Blitz versus Standard). There is no such thing as rated for one player but not the other.
I am confused about the rating system. I lost a game against a player who was not rated before. He jumped from 1200 to 1660 points after his first rated match, I went down from 1670 to about 1650. I won the next match against the same player, but this game was not rated for me, only for him, although the table says the game had been rated. ????