Example schema for my question is given at SQLFiddle and as follow:
CREATE TABLE `players` (
`player1id` int(11) NOT NULL,
`player2id` int(11) NOT NULL,
This ought to give you what you're looking for:
SET @PlayerId = 1;
SELECT `player2id` AS 'Other Player ID'
FROM `players`
WHERE `player1id` = @PlayerId
AND `player2id` != @PlayerId
UNION
SELECT `player1id`
FROM `players`
WHERE `player2id` = @PlayerId
AND `player1id` != @PlayerId;
SET @PlayerId = 5;
SELECT `player2id` AS 'Other Player ID'
FROM `players`
WHERE `player1id` = @PlayerId
AND `player2id` != @PlayerId
UNION
SELECT `player1id`
FROM `players`
WHERE `player2id` = @PlayerId
AND `player1id` != @PlayerId;