Nazgûl Battle-Mace

The last ability granted by Nazgûl Battle-Mace triggers whenever an opponent sacrifices a nontoken permanent for any reason, not just due to the annihilator ability.

If a replacement effect, such as that of Rest in Peace, causes a sacrificed nontoken permanent to be put into a different public zone than a graveyard, the last ability granted by Nazgûl Battle-Mace will still trigger and you will still put the card onto the battlefield under your control if its original controller doesn't pay 3 life.

If a creature with annihilator is attacking a planeswalker, and the defending player chooses to sacrifice that planeswalker, the attacking creature continues to attack. It may be blocked. If it isn't blocked, it simply won't deal combat damage to anything.