In the 6G Internet of Things (IoT) paradigm, unprecedented challenges will be raised to provide massive connectivity, ultra-low latency, and energy efficiency for ultra-dense IoT devices. To address these challenges, we explore the non-orthogonal multiple access (NOMA) based grant-free random access (GFRA) schemes in the cellular uplink to support massive IoT devices with high spectrum efficiency and low access latency. In particular, we focus on optimizing the backoff strategy of each device when transmitting time-sensitive data samples to a multiple-input multiple-output (MIMO)-enabled base station subject to energy constraints. To cope with the dynamic varied channel and the severe uplink interference due to the uncoordinated grant-free access, we formulate the optimization problem as a multi-user non-cooperative dynamic stochastic game (MUN-DSG). To avoid dimensional disaster as the device number grows large, the optimization problem is transformed into a mean field game (MFG), and its Nash equilibrium can be achieved by solving the corresponding Hamilton-Jacobi-Bellman (HJB) and Fokker-Planck-Kolmogorov (FPK) equations. Thus, a Mean Field-based Dynamic Backoff (MFDB) scheme is proposed as the optimal GFRA solution for each device. Extensive simulation has been fulfilled to compare the proposed MFDB with contemporary random access approaches like access class barring (ACB), slotted-Additive Links On-line Hawaii Area (ALOHA), and minimum backoff (MB) under both static and dynamic channels, and the results proved that MFDB can achieve the least access delay and cumulated cost during multiple transmission frames. Keywords: 6G; Internet of Things; grant-free random access; NOMA; dynamic backoff