If a monster is to be banished by D.D. Warrior effect it considered destroyed battle?

No, a monster banished by D.D. Warrior's effect is not considered destroyed by battle.

Here's why:

* D.D. Warrior's effect specifically banishes the monster. It doesn't say the monster is destroyed by battle.

* Banishing is a separate effect from destroying. While both remove a monster from the field, they have different implications for the game.

While the monster is removed from the field, it is not destroyed by battle, and therefore effects that trigger on destruction by battle will not activate.