If my Ruined Rex deals damage to a 6 might unit, does it die from the deathnell trigger before it gets healed?

No, the unit will not die from the Deathknell trigger before it gets healed.

According to the combat cleanup sequence established in official RiftJudge FAQ #10018 and FAQ #10069, the Deathknell ability of Ruined Rex resolves after the healing step of the Combat Cleanup.

Here is the step-by-step breakdown of how this happens:

1. Combat Damage Step: Combat damage is dealt.
2. Triggering Deathknell: Ruined Rex is killed; his Deathknell trigger is added to the chain as a pending item.
3. Killing Units: Lethal units are moved to the trash.
4. Healing: Surviving units on the battlefield are healed (Rule 461.1.a.1).
5. Resolution: Only after healing is complete does the game return to the FEPR (Finalize, Execute, Pass, Resolve) process to resolve the pending Deathknell trigger on the chain.

Because the healing occurs in step 4 and the resolution of the damage effect occurs in step 5, any damage marked on a surviving unit during combat is cleared before Ruined Rex's Deathknell ability deals its 4 damage.