Board Thread:Questions and Answers/@comment-10138327-20170424165650/@comment-27282915-20170424210150

It counts as destruction from a monster, so yes, you will draw a card.

Purgatory Knights, Eval Grebe Dragon needs to be destroyed by a monster effect in order to activate his ability. Since Sword Skill, Zanteisettetsu grants the monster [Counterattack], the monster, using [Counterattack], will destroy Eval Grebe, allowing you to draw a card.