It looks like the HWY is actually 372, not 316. You can exit onto 372 just after I-Dong and it does follow a river just like the instructions say.
This appears to be the parking lot https://goo.gl/maps/Se7RPqAzgaF2
of 백운계곡 (Baekeun Gyegok).
I've never been there so take that with a grain of salt.