Learn Hardcore Portuguese (Brazil): Eles ganharam o jogo ontem, e o treinador os parabenizou. - They won the game yesterday, and the coach congratulated them.

Ganharam is the simple past (preterite) 3rd-person plural form of ganhar. It shows that they (the players) completed the action of winning the game yesterday. In Portuguese preterite endings for –ar verbs you have –ei for eu, –ou for ele/ela, –amos for nós, and –aram for eles/elas.

What role does ontem play in the sentence, and can it be placed elsewhere?

Ontem means yesterday and functions as an adverb of time, telling us when the game was won. You can move it for emphasis:
• Ontem, eles ganharam o jogo
• Eles ganharam o jogo ontem
Both word orders are grammatically correct.

Why do we say o jogo with the definite article o? Could we use um jogo instead?

Using o jogo refers to a specific match (the one they played). If you talk about any game in general, you could say um jogo, but that makes it non-specific: Eles ganharam um jogo ontem.

Why is the subject pronoun Eles included at the beginning, and is it always necessary?

Portuguese is a pro-drop language, so you can omit the subject pronoun when the verb ending makes it clear. You could say Ganharam o jogo ontem, e o treinador os parabenizou and still be understood. Including Eles adds clarity or emphasis, especially for learners.

What is the pronoun os in os parabenizou, and what does it refer to?

Os is a masculine or mixed-gender direct object pronoun meaning them. It replaces a noun like os jogadores or the pronoun eles to avoid repetition. Since parabenizar takes a direct object, o treinador parabenizou os jogadores becomes o treinador os parabenizou.

Why is os placed before parabenizou instead of after it?

In modern Brazilian Portuguese, clitic pronouns typically precede the verb (proclisis) in everyday speech. Although prescriptive rules often teach placing pronouns after the verb (enclisis) in main clauses without triggers, nearly all Brazilians say os parabenizou rather than parabenizou-os in conversation.

Could we write parabenizou-os instead of os parabenizou, and is there any difference?

Yes. Parabenizou-os (enclisis) is grammatically correct and more common in formal or written Portuguese. It carries the same meaning as os parabenizou, but the latter is more idiomatic in spoken Brazilian Portuguese.

What are alternative ways to express congratulate someone in Portuguese besides parabenizar?

You can say dar parabéns a alguém (give congratulations to someone), using the indirect-object pronoun lhes: dar-lhes parabéns. Another option is felicitar, which is a bit more formal: o treinador os felicitou.