To be fair, though, the set-up doesn't state whether Sabretooth has an adamantium skeleton or not.
This is indeed true.
Large In Charge hasn't told us whether or not if Creed has adamantium bones. But even still, his healing factor has been incredibly hindered because of it. As a matter of fact, I am even wondering how Creed is still alive if his healing factor is inferior to Wolverine's, that he has survived the procedure. I'm thinking he should've died from that if Logan was barely able to survive the procedure.
But even with the adamantium bones, there are other ways for Kintaro to win. The brain can be shaken inside the adamantium skull, and in turn cause severe head trauma to someone like Sabertooth, and even Wolverine. As a matter of fact, I believe MarvelFan15 or Marvel Man provided scans where the Hulk had punched Wolverine hard enough for his brain to be shaken and the walls of his adamantium laced skull were actually damaging Wolverine's brain, making him effectively out of the fight.
Kintaro could possibly do the same, considering his strength and durability which is greater than Goro's.