マイクがそのゲームに勝ってみんな驚いたって英語でなんて言うの？

Everyone was surprised that Mike won the game. が正しい文章です。 Everyone was surprised/shocked when Mike won the game もいいと思います。 that もしくは when がなくても文章が成り立ちますが、that や whenが入ると文の運び方がより良いと個人的に思います。

"マイクがそのゲームに勝ってみんな驚いた" - Everyone was surprised that Mike won the game. - Mike won the game and everyone was surprised. （順番を逆にする） You can omit "that" from the sentence - Everyone was surprised Mike won the game. ー＞もっとカジュアル・話し言葉になります。