The code of conduct, for reference:
A paladin must be of lawful good alignment and loses all class abilities if she ever willingly commits an evil act.
Additionally, a paladin’s code requires that she respect legitimate authority, act with honor (not lying, not cheating, not using poison, and so forth), help those in need (provided they do not use the help for evil or chaotic ends), and punish those who harm or threaten innocents.
That's from 3rd edition, which is what Goblins is based on. 5th edition added some alternate oaths.
The whole class has a tendency to spark morality debates, heh. DND players argue about the exact nature of the alignments even *without* a player's class abilities relying on the answer.
It's possible the trick is the word "willingly". When Big Ears struck the time-golem of Vorpal (IIRC), he didn't lose his paladin powers, even though the act was evil enough to unseal the axe of Prissan. He didn't do evil on purpose. So Kore probably believes that he never does evil (particularly since he spends most of his dialogue justifying his actions as righteous).
He also does a pretty good job following the second half of the code... By the letter, anyway. Torture isn't honorable to most people, but the code doesn't mention it.
A lot of GMs would depower Kore anyway. The powers are (almost always) granted by gods, who would presumably frown on even the most self-righteous evildoer.
But this world is sad. (And technically you can be a paladin/cleric who worships an alignment itself, not a god).
(3.5 edition also evil/chaotic paladins as an optional rule, but they're pretty obscure, and I think Thunt outright said Kore isn't that.)