Not being familiar with Kyng, I agree that it is in the same style as the song in the op, but still don't hear how that is metalcore. That song is especially giving me some Alice in Chains and Soundgarden feelings. Three minutes in that changes but that's not really the predominant sound there.
EDIT: I'm assuming now that by "older-era metalcore" you're referring to Earth Crisis and such. Some of those bands had some Sabbath influence as well, but I'm not hearing where the influence went backwards to this kind of alternative metal.