The emerging 5G New Radio (NR) cellular systems that may operate in millimeter-wave (mmWave) frequency bands are expected to offer larger bandwidths. They are to be deployed in densely crowded environments, where the traffic load has a high degree of variability, which may introduce capacity bottlenecks. One of the options to alleviate the latter is to concurrently utilize the radio resources available in unlicensed mmWave bands, e.g., at 60 GHz. In this work, we address the coexistence of mmWave-based NR Unlicensed (NR-U) and WiGig technologies and account for the mmWave-specific directionality, propagation, and blockage effects. By further incorporating the features of duty cycling and random access operation, we construct a mathematical framework, which is capable of characterizing the achievable data rates of the NR-U users that operate over both licensed and unlicensed mmWave spectrum simultaneously. Our numerical results demonstrate that the rate attained by such devices is primarily regulated by the initial contention window size that, in its turn, heavily depends on the system and environmental parameters. We report the optimal contention window values for a wide range of blocker and user densities as well as antenna array configurations.