If Glasc Mixologist is defending and died at a battlefield, does its Deathknell trigger and therefore allow its unit to be played at the same battlefield before losing ownership?

Yes, Glasc Mixologist's Deathknell trigger allows you to play a unit from your trash to the battlefield, which can help you maintain control of that battlefield.

The Ruling

According to Rule 734.1.d.2, Deathknell triggers are added to the chain as a Pending Item before the unit is moved to the trash. Because the trigger is placed on the chain during the cleanup process (specifically during the "Handle outstanding board state" step, Rule 322.3), the game pauses to allow the chain to resolve.

If the Deathknell effect allows you to play a unit to that battlefield, you will have a unit present there when the game checks for control, allowing you to retain ownership of the battlefield.

Sequence of Events

1. Combat Damage: Damage is assigned to Glasc Mixologist.
2. Cleanup Begins: The game enters the cleanup phase (Rule 322).
3. Deathknell Triggers: Before Glasc Mixologist is moved to the trash, its Deathknell ability triggers and is added to the chain as a Pending Item (Rule 322.3 and Rule 734.1.d.2).
4. Chain Resolution: The chain is finalized and resolves (Rule 322.12). You resolve the Deathknell effect, allowing you to play a unit from your trash to the battlefield.
5. Control Check: After the chain resolves and the cleanup continues, the game checks for control of the battlefield. Because you successfully played a unit there, you still have a unit present, and you maintain control of the battlefield.

Note: I could not fully verify this ruling against the retrieved rules.