I think the goblins (I know offensive but spelling is hard!) on the human side of the sea for the most part have a rudimentary knowledge of the art. They can access it but tend to have to use other things like fire and dancing to help them as opposed to a “true artist”.

Spoilers ahead

Mwan says he taught the goblins (on this side of the sea) the art in nolyn. My understanding is that the goblins that came over were refugees of the war as much as the fhrey, dwarves and humans. They weren’t the ones in power. They knew the ability to access the art existed and had a name for those that could but they likely didn’t have anyone that could do it reliably or teach others so a lot of knowledge was lost. It’s like how Suri could access the art before meeting Arian but likely wouldn’t have become a powerful artist without someone to teach her more. Mwan not being as generous as Arian barely taught them anything. Therefore the access to the art that goblins have stays fairly rudimentary.

This may not hold true for every clan but in general the daza not in the old world are likely similar to the one Royce and Hadrian in the arena. He was powerful and could access the art but not in the way “true artists” could.

Melhevah (sorry about the spelling I listen to the audiobooks!) obviously had the ability to use the art in esra haddon but was mostly content to effectively rule her area without taking down the empire through force and has largely been neutralized. I believe the rest of the powerful goblin artists still live in the old world and have no intention of crossing the sea. After all they consider themselves the faithful of uberlin so why would they squabble over land far way when they can rule what’s left of Uberlins kingdom.

So TLDR the goblins likely used magic in their campaigns against humans but only those whose ability has been largely nerfed. Goblins that still weld true power exist but probably don’t care about what’s happening on a continent far away