I am also having trouble seeing how the gunslinger is doing that much damage if the number you quoted is correct its hard to imagine even at that level.
Factoring in his class gunslinger 11
He should have 6 feats from levels
He should have 2 bonus feats from gunslinger.
So let us assume the gunslinger has the normal feats most people would take as a gunslinger.
Dead Aim (at his level it would be -3 on attacks for a +6 damage)
Rapid Reload (free reloading with cartridges on the pistol)
Let us also assume for whatever reason he has both barrels of his double barrel enchanted at +3 (yes double barrels function like double weapons)
Let us also assume he has a dexterity of 20 so a modifier of +5 which we would add to the damage with the gun.
Assuming he isn't using any other damage or further attacks this round then he would be doing the following damage.
1d8+14 / 1d8+14 - firing at +11 (bab) + 5 (dexterity) +3 (mw properties) +1 for size -4 for firing both barrels in same turn -3 for deadly aim = +13
1d8+14 / 1d8+14 - firing at +6 (bab) + 5 (dexterity) +3 (mw properties) +1 for size -4 for firing both barrels in same turn -3 for deadly aim = +8
1d8+14 / 1d8+14 - firing at +1 (bab) + 5 (dexterity) +3 (mw properties) +1 for size -4 for firing both barrels in same turn -3 for deadly aim = +3
Assuming he hits everything on all the hits he would be doing 90-132 damage a turn on full attacks.
This could be raised via other magic items etc, but at his base he's probably somewhere in this realm.
If you add in the two weapon fighting rules (which you shouldn't because explain reloading guns with both hands full) it gets even less likely to hit.
More realistically he maybe took rapid shot for one more attack or in this case 2 more shots with the double barreled pistol, but that would end up looking more like this:
1d8+14 / 1d8+14 - firing at +11 (bab) + 5 (dexterity) +3 (mw properties) +1 for size -4 for firing both barrels in same turn -3 for deadly aim -2 for rapid shot= +11
1d8+14 / 1d8+14 - firing at +11 (bab) + 5 (dexterity) +3 (mw properties) +1 for size -4 for firing both barrels in same turn -3 for deadly aim -2 for rapid shot= +11
1d8+14 / 1d8+14 - firing at +6 (bab) + 5 (dexterity) +3 (mw properties) +1 for size -4 for firing both barrels in same turn -3 for deadly aim -2 for rapid shot = +6
1d8+14 / 1d8+14 - firing at +1 (bab) + 5 (dexterity) +3 (mw properties) +1 for size -4 for firing both barrels in same turn -3 for deadly aim -2 for rapid shot = +1
Again assuming you hit everyone of your shots the damage would be 120 - 176
Even adding a +6 dexterity modifier item to the character it doesn't make much sense that would just change the first scenario to 108-150
and the second scenario to 144-200 damage again assuming all of these things hits, which again is very unlikely.
Also if not already stated at level 11 in a skull and shackles game of any pirate worth his weight in gold heard of a goblin gunslinger blasting people out of the water they would find a nice defense against this very fast. Im shocked you haven't run into more people wearing amulets of bullet protection or with monk body guards busting out catch arrows and deflect arrows.