At first, Kim Jin Seok had confidently concluded that Satoshi was relatively weaker than him, and because of that, he made one fatal mistake— he fought on the same level as him.
There were plenty of chances wherein he could've taken the opportunity of beating Satoshi down, not letting him have a moment's rest while he pretended to be weak. But he chose not to. Somehow, his subconscious defaulted into fighting on even ground as Satoshi. It wasn't in terms of underestimating or overestimating him, but leveling himself with Satoshi as if that would give him the victory.
As for Satoshi, he was doing better than Kim Jin Seok despite acting like he was inferior to him. The reason for that was— he already knew how strong Kim Jin Seok was as a beast tamer, which is why he never underestimated him. Of course, one could debate that the two of them were approximating each other's strength, but it was apparent Satoshi did better than Kim Jin Seok in that regard.
At this point, everyone already knows who'd win :/