Attracted by the advantages of Non-Orthogonal Multiple Access (NOMA) in accommodating multiple users within the same resource, this paper investigates the power allocation problem for Machine Type Devices (MTDs) in a Hybrid NOMA system. Particularly, we consider a densely deployed network in which the devices are divided into orthogonal coalitions. Firstly, the power control problem is modeled as a differential game. Then, we formulate the proposed game as a Mean Field Game (MFG) in order to handle massive Internet of Things (IoT) access scenarios. Furthermore, we design an iterative algorithm that paves the way for distributed control in which the devices can appropriately regulate their transmit power in response to brief information received from the Base Station (BS). The analysis of the proposed approach is conducted through coupled equations, namely the Hamilton-Jacobi-Bellman (HJB) and the Fokker-Planck-Kolmogorov (FPK). Our simulation results prove the convergence of the proposed power control strategy and spotlight the robustness of our formulated MFG.