Rinko was an early series antagonist that ultimately got defeated by Sanyou Shin.
Time of introduction doesn't mean anything in Kingdom. It's not a shounen battle manga following the same tropes of progression where each new adversary is stronger than the last. It's never been that way.
Hou Ken was an early antagonist. Ri Boku still remains.
In fact, pretty much all of the best generals of Kingdom were introduced early. Ren Pa, Ou Sen and Kan Ki were all introduced in the same arc. Most of the strongest fighters were also introduced early on (Hou Ken, Ou Ki, Mou Bu, Tou, Kyou Kai, Yo Tan Wa, Ou Hon, Ba Jio, etc).
As for Sanyou Shin - that version of Shin had already faced monsters like Ran Kai and Hou Ken. He had fought Kyou Kai at that point already. From the onset, Shin lacked many things, but fighting ability wasn't one of them. He has
always been a freak in this regard.
Even so, it needs to be acknowledged Hara wrote the plot in a way in which Rin Ko lost two fingers and sustained an injury to the neck/shoulder before he died on Shin's and Ou Hon's combined 5th opportunity fighting him.
It was a legitimate loss but Hara certainly went out of his way to give Rin Ko a respectful exit.