We present a detailed analysis on the influences of short branches on the structural, conformational, and dynamical properties of short-chain branched (SCB) ring polyethylene melts using atomistic molecular dynamics simulations. Ring polymers exhibit the compact molecular structures compared to linear polymers, due to their intrinsic closed-loop geometry and an additional effective pressure via the nonconcatenation constraints between ring chains. Importantly, short branches located along the chain backbone are found to make the overall ring structure further compact via the intrinsically compact branched architecture and the fast random movement of short branches that constantly disturbs the chain conformation. Notably, the effects of short branches on the structural compactness for SCB ring polymers appear to be quantitatively very similar to those of SCB linear polymers. We also find that the structure and relaxation of the unentangled SCB ring and linear melt systems can be reasonably well characterized with the Rouse model, regardless of the short branches. Meanwhile, certain distinctive structural and dynamical features of the Rouse normal modes appear for the SCB ring systems in association with the separate effects of short branches and ring topology. Detailed analysis on several distinct torsional modes around branch points along the chain backbone reveals noticeable differences among the torsional modes with respect to the probability distributions of the gauche- and trans-states and the torsional dynamics. This is ascribed to an extra torsional stiffness imposed by the short branches. Additional analysis of the interatomic pair distribution functions for the SCB systems further confirms the fundamental role of short branches in determining the local and global chain structure.