MYSQL search for each name in 2 columns and add values associated for each player
Glorfindel's answer is good within the parameters of your question, but I'll talk a bit about how else you could have designed it, in case that's helpful.

Basically, having a single table with player1 and player2 isn't great because the two players have the same relationship to the game so it should be represented the same way. If it's important to keep track of which one was #1 and which was #2, then it's probably better to think of that as an attribute of the player's membership in the game. 

CREATE TABLE `player` (`id` PRIMARY KEY, ...);

CREATE TABLE `game_results` (`id` PRIMARY KEY, ...);

CREATE TABLE `game_player` (
  `game_id`,
  `player_id`,
  `destroyed`,
  PRIMARY KEY (`game_id`, `player_id`),
  FOREIGN KEY (`game_id`) REFERENCES `game_results` (`id`),
  FOREIGN KEY (`player_id`) REFERENCES `player` (`id`),
  ...
);


Some open questions remain from there.


Where should the results be recorded?


You could just have a nullable foreign key winner from game_results to game_player (id).
You could have an attribute result of game_player. This could be an enum if you're in MySQL 5.7, or a foreign key to a small table of possible results. I'd prefer this because it would better accommodate draws and annulments. 

The join-table design naturally allows for games with more than two players. Whether or not that's good depends on the situation. Assuming we want to limit the number of players, how would we do that?


Add another enum or foreign key to an enum table representing the idea of "player 1" and "player 2". Add a UNIQUE KEY game_player (game_id, player_number). This is what I would suggest.
Add a FOREIGN KEY game_player(partner) REFERENCES game_player(id). This would work for your current situation, but isn't an open-ended solution.
You can't use a CHECK constraint in MySQL. This is one of the reasons I dislike MySQL. Here's the reference.



In any case, the final query you're trying to build would look something like

SELECT gp1.player_id, SUM(gp1.destroyed) AS Fmov, SUM(gp2.destroyed) AS Fmov 
  FROM `game_player` gp1
  [LEFT | INNER] JOIN `game_player` gp2
    ON gp1.game_id = gp2.game_id
      AND gp1.player_id &lt;&gt; gp2.player_id
  [WHERE gp1.result in (`win`, `loose`, `tie`)]
  GROUP BY gp1.player_id;