Because damage remains marked on a creature until the damage is removed as the turn ends, nonlethal damage dealt to Master of Etherium may become lethal if other artifacts you control leave the battlefield during that turn, and damage dealt to other artifact creatures you control may become lethal if Master of Etherium leaves the battlefield during that turn.

The ability that defines Master of Etherium's power and toughness applies in all zones, not just the battlefield.

As long as Master of Etherium is on the battlefield, its ability will count itself.