Does deathtouch work when dealing combat damage to a planeswalker?

Deathtouch is a static ability that states any amount of damage dealt by a source with deathtouch is enough to destroy a creature (CR 702.2b). The key word is creature. Planeswalkers are not creatures, so the deathtouch rules simply do not apply to them.

When a creature with deathtouch deals combat damage to a planeswalker, the damage is still redirected normally — it removes that many loyalty counters from the planeswalker (CR 120.3c). If the planeswalker reaches zero loyalty counters, it is put into its owner's graveyard as a state-based action (CR 704.5i). But this happens because of the counter-removal rule, not because of deathtouch.

So even 1 damage from a deathtouch creature will remove 1 loyalty counter — but 1 damage does NOT automatically destroy the planeswalker the way it would destroy a creature with 10 toughness. The planeswalker only dies if its loyalty reaches zero.

Example: Your opponent controls a Liliana with 5 loyalty. You attack it with a 1/1 deathtouch snake. It deals 1 combat damage, removing 1 loyalty counter (Liliana goes to 4 loyalty). Liliana survives — deathtouch provided no extra benefit here.

In summary, deathtouch is purely a creature-destruction mechanism (CR 702.2b, 702.2c) and has no additional effect when the damage is applied to a planeswalker.