The description says, "The first unit to deal damage to an enemy while no units are deathmarked is inflicted with deathmark until the end of battle...."
From my most recent battle:
GAS takes a turn, his first attack kills by Sith, who was deathmarked. There are now no units deathmarked. Then he immediately uses another ability, damages another character and ... is not deathmarked.
Whether it's a bug or whether the description is written wrong, I don't know, but GAS damaged a unit while no others were deathmarked and did not get deathmarked, so it sure as heck isn't working as written.