This paper introduces DEM-Engine, a new submodule of Project Chrono, that is designed to carry out Discrete Element Method (DEM) simulations. Based on spherical primitive shapes, DEM-Engine can simulate polydisperse granular materials and handle complex shapes generated as assemblies of primitives, referred to as clumps. DEM-Engine has a multi-tier parallelized structure that is optimized to operate simultaneously on two GPUs. The code uses custom-defined data types to reduce memory footprint and increase bandwidth. A novel "delayed contact detection" algorithm allows the decoupling of the contact detection and force computation, thus splitting the workload into two asynchronous GPU streams. DEM-Engine uses just-in-time compilation to support user-defined contact force models. This paper discusses its C++ and Python interfaces and presents a variety of numerical tests, in which impact forces, complex-shaped particle flows, and a custom force model are validated considering well-known benchmark cases. Additionally, the full potential of the simulator is demonstrated for the investigation of extraterrestrial rover mobility on granular terrain. The chosen case study demonstrates that large-scale co-simulations (comprising 11 million elements) spanning 15 seconds, in conjunction with an external multi-body dynamics system, can be efficiently executed within a day. Lastly, a performance test suggests that DEM-Engine displays linear scaling up to 150 million elements on two NVIDIA A100 GPUs.