In this paper, the problem of optimized beam alignment for wearable device-to-device (D2D) communications over millimeter wave (mmW) frequencies is studied. In particular, a noncooperative game is formulated between wearable communication pairs that engage in D2D communications. In this game, wearable devices acting as transmitters autonomously select the directions of their beams so as to maximize the data rate to their receivers. To solve the game, an algorithm based on best response dynamics is proposed that allows the transmitters to reach a Nash equilibrium in a distributed manner. To further improve the performance of mmW D2D communications, a novel quantum game model is formulated to enable the wearable devices to exploit new quantum directions during their beam alignment so as to further enhance their data rate. Simulation results show that the proposed game-theoretic approach improves the performance, in terms of data rate, of about 75% compared to a uniform beam alignment. The results also show that the quantum game model can further yield up to 20% improvement in data rates, relative to the classical game approach.