Traditionally:

European
– Dreaming of game in generally: means prosperity;
– To shoot: you will see your heart’s desires fulfilled;
– Also shooting of game: points to lucky businesses;
– If you can’t shoot or kill game in dream: indicates a bad planning and losses.

Hindu
– To see game in dream: your work will be succeed;
– In general dreaming of game: you will live a free life;
– To shoot: you will not suffer any hardship.

Arabian
– To see hunt of game: rivalries will upset you;
– To shoot game yourself: you know how to make your fortune.

* Please, see also meaning of trap and hunting.