And also running the clock down.
Resignation used as a tactic?

I just played a game where one guy got a mate and the other two resigned. When I was about to capture one of the kings, the remaining opponent resigned. The game didn't even last three moves.
This is clearly still a mistake in the logic of the game. It makes no sense that I can simply resign when only two players are left and I win automatically, if I got more points

This is clearly still a mistake in the logic of the game. It makes no sense that I can simply resign when only two players are left and I win automatically, if I got more points
True.

This is clearly still a mistake in the logic of the game.
I disagree. I think it is important to keep in mind that the logic of 4 player chess is different from that of normal chess.
You are right: This would be a mistake in the logic of normal chess - because the objective there is to win or at least not lose. In 4 player chess, however, the objective is to get the majority of points regardless if you win or lose, and so it makes perfect sense in the game (and like Martin0 says), it even supports the logic of the game by highlighting the objective of gathering the most points: by making points more valuable. It will simply be in all players' interest not to eliminate each other if there is one player with a vast majority of points.
It's the same rule of thinking ahead and analyzing potential outcomes as in normal chess, but other and more complex potential outcomes to consider. Now, you must be able to analyze your interests of attacking different players and their interests of attacking you at different points of time, and the opportunity cost. Examplewise, either you kill a queen right away and get 9 points, or you kill that queen after that queen has killed some of the most threatening opponent's pieces, get 9 points and a weaker third opponent.

I just resigned with 3 players remaining. One player had only 2 pawns left and I was ahead with more than 32 points. I also had only pawns left. I got the king from a player that left early and then basically exchanged my whole army with one player. The guy with 2 pawns left resigned before the guy with a big army had time to take my king and since he was more than 15 points ahead of the big guy he got second place. The last man standing came in third.

- Rule says: "When a player resigns or times out, leaving two or more active players on the board, their King remains in color and is still worth +20 to whoever can capture it; but if there are only two players remaining, the remaining player will be given +20 points"
There was only 2 players left. The other one times out but I did not get 20 points. The points remain the same and game over, the timed-out guy won...Something does not sound right there. From the rules, and from logic, I should have got 20 points, no?

Yes, agreed. I think they did not revert the rule back, maybe they forgot that the last player does not have to capture the king to get 30 points? I got the same, was 20 points out of the lead and would win easily. When my opponent "resigned" both players were given 3 points...like if this is supposed to be a draw for the last two players...FIDEdigno had 50 and I had 30, he resigned and got 3 points for each of us, unfair.
Since checkmate or the last man standing isn't the way to win, resignation doesn't necessarily lose. Some players use this as a trick to win (when there are only 2 players left) when he/she has more points and can afford to give 15 points to the opponent by resigning, and still winning by points. Wouldn't this be a little annoying?