Use a seperate column to indicate the join condition
SELECT t.importid,
case
when t.importid = g.home
then 'home'
else 'away'
end as join_condition,
g.network,
g.date_start
FROM game g
INNER JOIN team t ON (t.importid = g.home OR t.importid = g.away)
ORDER BY date_start DESC
LIMIT 7