My father gave me a computer game.

Literal

Father [from-から] me [to-に] computer-game [subject-が] was-given.

~から~に~が与えられた is a passive giving construction: 'from father, to me, a game was given.' 与えられる is the passive of 与える ('to give,' formal). The subject is the thing given, not the giver — a different framing from ~をもらった.