The effect of "Doomkaiser Dragon" targets 1 Zombie-Type monster, both in your opponent's GY and while it is on the field.
Destroying the Special Summoned Zombie-Type monster when "Doomkaiser Dragon" is removed from the field does not start a Chain.
If an effect is chained that flips "Doomkaiser Dragon" face-down, the targeted Zombie-Type monster is still Special Summoned and it is no longer targeted by "Doomkaiser Dragon" while on the field.