In December 2019, the 3GPP defined the road-map for Release-17, which includes new features on the operation of New Radio (NR) in millimeter-wave bands with highly directional communications systems, i.e., up to 52.6 GHz. In this paper, a system-level simulation based study on the coexistence of NR-based access to unlicensed spectrum (NR-U) and an IEEE technology, i.e., 802.11ad Wireless Gigabit (WiGig), at 60 GHz bands is conducted. For NR-U, an extension of NR Release-15 based model is used such that the 60 GHz regulatory requirements are satisfied. First, the design and capabilities of the developed open source ns-3 based simulator are presented and then end-to-end performance results of coexistence with different channel access mechanisms for NR-U in a 3GPP indoor scenario are discussed. It is shown that NR-U with Listen-Before-Talk channel access mechanism does not have any adverse impact on WiGig performance in terms of throughput and latency, which demonstrates that NR-U design fulfills the fairness coexistence objective, i.e., NR-U and WiGig coexistence is proven to be feasible.