-- set up test data
CREATE TABLE Games (
    Winner INT NOT NULL,
    Loser INT NOT NULL,
    ID INT PRIMARY KEY,
    CHECK (Winner <> Loser)
);
INSERT INTO Games VALUES
(456, 123, 1),
(789, 456, 2),
(101112, 789, 3),
(949596, 919293, 4),
(103104, 101102, 5),
(106107, 103104, 6); -- I assume your original screenshots had a typo

-- the actual query
WITH loopy AS (
    SELECT g.Winner, g.Loser, Level = 1
    FROM Games g
    UNION ALL
    SELECT g.Winner, l.Loser, Level = l.Level + 1
    FROM loopy l
    INNER JOIN Games g
    ON g.Loser = l.Winner
)
SELECT l.Winner, g.Loser, g.ID
FROM Games g
INNER JOIN (
   SELECT l.*, Priority = ROW_NUMBER() OVER (PARTITION BY l.Loser ORDER BY l.Level DESC)
   FROM loopy l
) l
ON l.Loser = g.Loser AND l.Priority = 1
ORDER BY g.ID;

// ... snip
ON l.Loser = g.Loser AND l.Priority = 1
ORDER BY g.ID
OPTION (MAXRECURSION 1000); -- added