"Killed by the game" is always an effect from a card controlled by a player, whether the card is a character, an event, a wall, or whatever. Unless "discard" is specified, the killed card should go to the magic pile of the player who controls the card with the instruction to inflict the wound. E.g. A Crusher who accidentally suicides goes into his own player's magic pile.
Swamp Orcs get magic for enemies (and friends) killed by vine walls.
Q: If a Unit is destroyed moving off a Vine Wall, who receives the Magic?
A: The Vine Wall's controller.