We present the fundamental molecular characteristics underlying the rheological behaviors of interfacial ring polymers in a wide range of flow strengths using atomistic nonequilibrium molecular dynamics simulations of confined ring polyethylene melts under shear. Ring polymer, with its intrinsic closed molecular topology, exhibits a weaker interfacial slip in the weak-to-intermediate flow regime as compared to its linear analogue because of the larger friction between the ring chains and the wall arising from a longer chain dimension in the neutral direction at the interface. In the intermediate flow regime, ring polymer displays, in addition to the standard out-of-plane wagging mechanism of local loops (similar to the linear polymer), a distinctive molecular mechanism (loop migration) wherein locally created chain loops propagate along the chain in the flow direction. This additional mechanism leads to a lesser degree of the overall decreasing tendency of interfacial slip in the intermediate flow regime. In the strong flow regime, interfacial ring chains display rotation and tumbling dynamics at the wall. However, in contrast to the linear polymer, the ring polymer exhibits two distinct (parallel and vertical) loop tumbling dynamics depending on the angle of the loop-section plane relative to the vorticity plane. We further observed that at strong flow fields an interfacial chain is frequently coupled with other nearby interfacial chains, implicating an increased effective molecular weight of a moving interfacial chain thereby affecting the interfacial chain dynamics and properties. These dynamical features may enhance our understanding of various interfacial properties and phenomena in practical polymer processes.