Ultra-low latency and high reliability communications are the two defining characteristics of tactile Internet (TI). Nevertheless, some TI applications would also require high data-rate transfer of audiovisual information to complement the haptic data. Using millimeter Wave (mmWave) communications is an attractive choice for high data-rate TI applications due to the availability of large bandwidth in the mmWave bands. Moreover, mmWave radio access is also advantageous to attain the air-interface-diversity required for high reliability in TI systems as mmWave signal propagation significantly differs to sub-6 GHz propagation. However, the use of narrow beamwidth in mmWave systems makes them susceptible to link misalignment-induced unreliability and high access latency. In this article, we analyze the tradeoffs between high gain of narrow beamwidth antennas and corresponding susceptibility to misalignment in mmWave links. To alleviate the effects of random antenna misalignment, we propose a beamwidth-adaptation scheme that significantly stabilize the link throughput performance.