Learn Spanish (Latin America): Mis amigos hacen deporte aquí.

The verb hacer (to do/make) is only irregular in the yo (I) form, which is hago. For all other people, including the "they" form (hacen) used here for mis amigos, it follows the completely normal rules for -er verbs.

In English we usually say "play sports." Why does this sentence use hacer (to do/make)?

In Spanish, the standard way to say "play sports," "do sports," or "work out" is hacer deporte. You only use the verb jugar (to play) when you are naming a specific game or sport, like jugar al tenis (to play tennis).

Why is it mis amigos instead of mi amigos?

In Spanish, possessive words like "my" have to match whether the noun they describe is singular or plural. Since amigos is plural, you must use the plural form mis. If it were just one friend, it would be mi amigo.

Is it wrong to say hacen deportes (plural) instead of hacen deporte?

It is not wrong at all! You can absolutely say hacen deportes. However, Spanish speakers very often use the singular deporte to talk about sports or exercising as a general, uncountable activity. Both are perfectly natural.