This paper spotlights key design features of a novel Gigabit Wireless Mesh MAC protocol (GWM-MAC) for a new class of high-throughput backbone broadband wireless mesh networks operating in 60-80 GHz. The proposed protocol is based on the Spatial TDMA channel access scheme and defines several operating modes. The protocol is designed to serve the needs of a heavy-loaded backbone mesh network with a volatile traffic. GWM-MAC is suitable for transmitting data flows via multihop paths as well as for broadcasts and single-hop communications. For multihop flows-oriented communications the granted-to-requested ratio maxmin resource allocation criterion is utilized allowing fair schedules building in case of the large number of flows with significantly varying resource needs. The proposed protocol is very flexible and can be dynamically configured to serve the actual network needs.