Machine-to-machine (M2M) communications, which are considered as an integral part of the Internet of Things (IoT), are being more and more ubiquitous. Meanwhile, due to the advantages of cellular networks (e.g., excellent coverage and mobility/roaming support), cellular-enabled M2M communication is a promising solution for M2M-based applications. However, there are significant challenges in cellular-enabled M2M communications due to the special features of M2M-based applications [e.g., massive concurrent uplink transmissions, small bursty traffic, and the high requirements of energy efficiency (EE)]. On the other hand, non-orthogonal multiple access (NOMA) can simultaneously serve multiple users at the same frequency and time by splitting different users in the power domain and thus increase the number of concurrent connections. In this paper, we propose an energy-efficient resource allocation scheme with hybrid time division multiple access (TDMA)-non-orthogonal multiple access (NOMA) for cellular-enabled M2M networks. First, we configure the user equipments (UEs) as the machine type communication gateways (MTCGs). Then, we propose our time sharing scheme. Next, we formulate the resource allocation problems as a noncooperative game. Finally, in order to obtain the optimal EE of machine type communication devices (MTCDs) and UEs in the game to confirm the power allocation, we transform each non-convex optimization problem into the convex form by using nonlinear fractional programming and solve the transformed problem by Dinkelbach's method and Lagrangian duality theory. The simulation results show that our scheme can dramatically shorten the total transmission time at the cost of a little more total energy when compared to the existing works.