You can use an unstored calculation field with get ( CurrentTime ) in a relationship to bring up the next set of games in a portal, but it looks like you need some additional data to discriminate between current and previous games.
Tournament::CurrentTime < NextGames::TimeofGame (NextGames is a table occurrence of your imported tournament schedule)
AND Tournament::TournamentID = NextGames::TournamentID
would work in a portal for next games.
Tournament::CurrentTime > CurrentGames::TimeofGame (CurrentGames is a second table occurrence of the same schedule table.)
AND Tournament::TournamentID = CurrentGames::TournamentID
Might work for both current and previous games if you sort your portals in descending order by start time and simply specify that the previous games portal display 8 rows starting with row 9.