Does deathtouch work when a creature deals combat damage to a planeswalker?

Deathtouch is defined in CR 702.2: any amount of damage dealt by a source with deathtouch is sufficient to destroy the damaged creature. The critical word is creature. A planeswalker is not a creature, so the deathtouch ability simply does not apply when combat damage is assigned to one.

When a creature attacks a planeswalker, combat damage dealt to that planeswalker removes loyalty counters equal to the damage amount (CR 306.7). The planeswalker is then put into its owner's graveyard if it has no loyalty counters (state-based action, CR 704.5i). This process is entirely unaffected by whether the attacking creature has deathtouch.

Deathtouch also does not grant any bonus against planeswalkers in terms of damage quantity needed — you still need enough damage to reduce the planeswalker's loyalty to zero, just as you would without deathtouch.

Concrete example: Your 1/1 deathtouch creature attacks your opponent's Liliana of the Veil, which has 3 loyalty. The 1/1 deals 1 combat damage, removing 1 loyalty counter. Liliana survives with 2 loyalty. Deathtouch did nothing here — you needed 3 total damage to finish her off, same as any other source.

In summary, deathtouch is exclusively relevant when dealing damage to creatures (CR 702.2b). It has no interaction with planeswalkers, artifacts, enchantments, or players.