This can be a messy requirement to implement. By having two FKs in the Games table you will need to create some UNION views or apply conditional logic to your queries to make sure you join Team to both applicable FKs in Game.
An alternative is to create a third table called "GameTeams" to implement a many to many relationship between Games and Teams. This may simplify some of your queries, but you will have to enforce a rule requiring that a game have no more than two associated team records.
So both methods have some drawbacks, and you'll just have to work around whichever one you choose.
If it's not practically useful, then it's practically useless.
, Team1.teamName as Team1Name
, Team2.teamName as Team2Name
JOIN Teams AS Team1
ON Team1.teamID = Calendar.teamID1
JOIN Teams AS Team2
ON Team2.teamID = Calendar.teamID2