On the other hand, if Cyclops Gladiator leaves the battlefield before the ability resolves, the ability continues to resolve. Cyclops Gladiator deals damage to the targeted creature equal to the power it had as it last existed on the battlefield.

Cyclops Gladiator’s ability triggers and resolves during the declare attackers step, before blockers are declared. If it survives, it continues to attack (presumably with some damage marked on it) and may be blocked.

If the targeted creature leaves the battlefield (or otherwise becomes an illegal target) before the ability resolves, the ability doesn’t resolve. Cyclops Gladiator isn’t dealt damage.