MySQL 5.7

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select version();

version()

5.7.39

create table mytable (id int, winnerid int, loserid int, gameid int);
insert into mytable values (1, 1, 2, 1), (2, 2, 1, 1), (3, 1, 2, 1), (4, 1, 2, 2), (5, 1, 3, 1);

Records: 5  Duplicates: 0  Warnings: 0

select winnerid, count(*) 
from mytable
where gameid = 1
and (winnerid, loserid) in ((1,2), (2,1))
group by winnerid;

winnerid
count(*)

1
2

2
1