Questions & Answers about Wir spielen gegen die Mannschaft.
Why is it die Mannschaft here? Doesn't the preposition gegen require the accusative case?
It is in the accusative case! The preposition gegen always forces the noun that follows it into the accusative. However, for feminine nouns like Mannschaft, the word for the is die in both the nominative (subject) and accusative (object) cases. The word for the only visibly changes its shape in the accusative case for masculine nouns.
How can I tell that Mannschaft is a feminine noun just by looking at it?
The ending -schaft is a very reliable clue. In German, nouns ending in -schaft are almost always feminine and use die. Another example you might know is die Freundschaft (the friendship).
To make sure I understand the rule for gegen, how would this sentence change if we played against a masculine noun, like der Computer (the computer)?
Because gegen strictly takes the accusative case, the masculine word for the (der) must change to den. The sentence would become: Wir spielen gegen den Computer.
Does gegen only mean against in sports or games?
It means against in almost any kind of opposition. You can use gegen for playing against a team, being against an idea, or even physically bumping into something, like walking against a wall.