Do they gain the benefit when a player chooses to engage them? an example of this would be forest spider.

"after forest spider engages a player it gets +1 attack until the end of the round."

Does he still gain this benefit when i choose to engage him?

Short answer - Yes

Long answer - from page 16 of the rule book

Whether an enemy is engaged through an engagement
check, through a card effect, or through a player’s
choice, the end result is the same, with the enemy
and the player engaging one another. In all cases, the
player is considered to have engaged the enemy and the
enemy is considered to have engaged the player.