Dergaix takes a 5 foot step in the Down direction back into melee range.

Dergaix Full Attacks with Disarm attempts, attempting to steal the greatsword.

Dergaix doesn't have the Improved Disarm feat.

Gubbirk gets an Attack of Opportunity.

Greatsword: 1d20 + 12 = 13. Miss.

Bite to Disarm: 1d20 + 11 = 28 > 21, Succeeds.
Claw: 1d20 + 11 = 24 > 23. Hit.
1d4 + 3 = 4.
Claw: 1d20 + 11 = 20. Miss.

Gubbirk now has 22 HP.
Dergaix is now holding a +1 greatsword in his mouth.

um...

Gubbirk would like that guy with all the strategic advice to come back.

If you resort to using your throwing axes as a melee weapon:
You cannot realistically hope to kill Dergaix before he kills you.

If you retreat underground:
Your hidey hole is around 80 feet away. He'd only get to hit you once before you reach it.
You can't just hide there. That's admitting defeat, and eventually your energy resistance would run out, or he'd suffocate you in smoke.

If you run for the hills:
Dergaix can move faster than you, and gets a free attack off every round.
You would still get quite far though, and might have an opportunity to enter stealth.
Got any invisibility potions on you?

Going back to his hole means he can grab another greatsword.

It wouldn't be +1, but it'd still let him use all his greatsword-specific weapon training, and that's where a lot of his damage output is coming from.

That could work, although if you just want a greatsword, there's one right in front of you.

Gubbirk attempts a disarm.

Dergaix gets an attack of opportunity?

He'd like to bite him, but there is a sword in his mouth.
So claw, he guesses.

Claw: 1d20 + 11 = 25. Hit.
1d4 + 3 = 4

Disarm: 1d20 + 9 = 27. Success.

Gubbirk now has 18 HP.
Gubbirk is now holding a +1 greatsword in his mouth hands.

If he just stands here, he dies next round to a Full Attack, doesn't he?

Probably not in one round, no. There's only a 20% chance of that.

Gubbirk uses his move action to get 30 feet away, in the forest direction.

If he runs after him, he only gets one attempt at a disarm, Gubbirk gets an AoO either way, and either a full attack if he fails the disarm or runs again after stealing it back again, yes?

Both of you can succeed on disarm attempts 45% of the time.
If it's a Full Attack, you'd succeed 83% of the time, but you can't make a full attack after chasing him down.

If that first disarm fails, he gets an AoO and a Full Attack, for a 30% chance of killing you immediately.

If it succeeds, he has a 45% chance of getting the sword back again, putting you right back where you're at now but you've taken an extra AoO worth of damage.

If it succeed and he fails though, you can totally kill him before he kills you.

And if Dergaix just lets him run away?

He might come back and kill you in your sleep.

He's not Nub, but he still has +15 to Stealth.

The God Trekzilk worships is Lawful Evil, but He is not Asmodeus.
He does not care for contracted obligations or formal oaths.
Submission is done to Power alone, and dies with it, regardless of what might have been otherwise.

Still, Trekzilk is not yet perfected in Lawful Evilness, and he feels more than zero concern in the welfare of someone he has known and fought beside for years, even though they are not technically related.

He has the wisdom to ignore this.

In which possible future does Trekzilk end up with more power, more resources, more opportunity to assert himself over others? In which possible future do Trekzilk's children and Trekzilk's people have more chance to survive?

- The Goblins end up ruled by Gubbirk, glorious in victory but shamed by the effort it took to obtain. The group will be wanting more independence. The younger Goblins will see him aging, and will be looking for a new leader to replace the old.

- The Goblins end up ruled by a Red Wyrmling. It ages slowly, and will be around a while. It cannot speak Goblin, and so must rely on the few Goblins that can cast Comprehend Languages until they can learn to speak it naturally. Trekzilk ends up the essential middle-manager between underlings who have no way to complain to their overlord and a master who has no reason to care even if they could.

- Either Gubbirk escapes alive and returns to try again, or the Goblins take his side visibly but the Dragon escapes alive, and in either case a larger conflict beyond this duel will grow until it destroys his people entirely. Trekzilk will die with it, and likely most of his children too.

- Neither survives, Trekzilk slays the winner while weakened and assumes power himself. He may get a Chief's share of power and resources, but he is not confident a Cleric 5 can keep them safe from the rest of the world for long, and his own apparent weakness will be his death soon enough if he tries to push his authority too far.

He has some ability to change the outcome, a Bless here or a Bane there, or a Barbed Chains. He is not confident it would be enough, and if he picks a side that loses anyway it would be the end of him.

He could order the tribe to attack one or the other, but they could not kill the Dragon, only chase it away for a while, and they would not eagerly kill their own chief.

Trekzilk has no good options. He will take no action.

Dergaix will move to 10 feet above him, but he will not close into melee on a round where he would not get to make a Full Attack.

Then he will keep running, not even bothering to throw an axe.

I'm not getting into range for you to Full Attack first.

If you're not going to fight me, I can fire breath every 2.5 rounds, half of which hit, dealing 2d10 - 10 or an average of 2.2 damage per attack.

It'd take me 9 hits spread over about 5 minutes to kill you, but I'll kill you long before the energy resist runs out.

He doesn't need 5 minutes to reach a thick group of bushes, and disappear behind them into a tunnel.

Crap.

He doesn't appear to be coming back out, or even cornered.

Dergaix will return and, lie to everyone that Gubbirk is dead?
No, that is a bad idea, easily disproven by Gubbirk existing.

He will explain that he has chased Gubbirk away, and that Gubbirk is banished from the village, and if anyone sees him tell him not to come back.