@OP: This sounds simply like Fischer time, in which both players are granted a time bonus after making every move. Your last several games in Live Chess were 2|1, which means both players get two minutes for the whole game, in addition to one extra second after every move.
If your opponent was taking less than one second to move consistently, then he would actually gain time.
This is not cheating; this is fair because both players have the potential to do this.
You probably already know this, so I don't mean to insult your intelligence, but if you don't, I am surprised, because you have completed thousands of games in almost three years on the site. Have you never encountered Fischer time before?
I would really like to know why is the computer cheation on time. I 'll give an example, which happened to me not once, but several times. The speed 2 min.game is before its conclusion. Material is even, nobody could go ahead. My time shows 35 the other player has only 20 sec. Suddenly the computer starts giving more and more time to my opponent. It goes so absurd that he finishes his "victory" with almost one minute to spare. As the game goes on, the computer goes virtually backwards calculating his time up instead of down. I don't dwell on the results too much, because 2 minutes game just isn't a serious chess, but I really wonder, why it goes like that. Why are certain players preffered? It's definitely not a fair play and it's certainly against the rules.