Does thousand tail watcher play ability count towards ezreal legend ability?

No — Thousand-Tailed Watcher's play ability doesn't count toward Ezreal at all, because it never chooses anything.

Ezreal's legend ability needs you to have "chosen enemy units and/or gear twice this turn with spells or unit abilities." Thousand-Tailed Watcher's ability is a unit ability (that source category is fine), but it reads "give enemy units -3 might this turn" — it affects a group defined by criteria, so no units are targeted or chosen (Rule 355.5.a, same principle as "Kill all gear" not being a Choice). It contributes zero to the count, not one.

For comparison, Bellows Breath counts because it makes you choose up to three specific units. Letting Watcher resolve and then trying to exhaust Ezreal won't work unless you've separately chosen enemy units/gear twice that turn with other spells or abilities.