Poderia ser?
$query="SELECT
m.MatchID,
m.MatchDate,
m.Team1ID,
m.Team2ID,
s.TeamID,
s.MatchID,
T1.TeamName as TeamName1,
T2.TeamName as TeamName2,
s.Score as Team1Score,
s2.Score as Team2Score
FROM TblMatch m
JOIN TblTeam T1 ON m.Team1ID = T1.TeamID
JOIN TblTeam T2 ON m.Team2ID = T2.TeamID
JOIN TblScore s ON m.Team1ID = s.TeamID AND m.MatchID = s.MatchID
JOIN TblScore s2 ON m.Team2ID = s2.TeamID AND m.MatchID = s2.MatchID
WHERE s.MatchID=$mid";