HPC systems are increasingly used for data intensive computations which exhibit irregular memory accesses, non-uniform work distributions, large memory footprints, and high memory bandwidth demands. To address these challenging demands, HPC systems are turning to many-core architectures that feature a large number of energy-efficient cores backed by high-bandwidth memory. These features are exemplified in Intel's recent Knights Landing many-core processor (KNL), which typically has 68 cores and 16GB of on-package multi-channel DRAM (MCDRAM). This work investigates how the novel architectural features offered by KNL can be used in the context of decomposing sparse, unstructured tensors using the canonical polyadic decomposition (CPD). The CPD is used extensively to analyze large multi-way datasets arising in various areas including precision healthcare, cybersecurity, and e-commerce. Towards this end, we (i) develop problem decompositions for the CPD which are amenable to hundreds of concurrent threads while maintaining load balance and low synchronization costs; and (ii) explore the utilization of architectural features such as MCDRAM. Using one KNL processor, our algorithm achieves up to 1.8x speedup over a dual socket Intel Xeon system with 44 cores.