A wide variety of data can be represented using third-order tensors. Applications of these tensors include chemometrics, psychometrics, and image/video processing. However, traditional data-driven frameworks are not naturally equipped to process tensors without first unfolding or flattening the data, which can result in a loss of crucial higher-order structural information. In this letter, we introduce a novel framework for data-driven analysis of T-product-based dynamical systems (TPDSs), where the system evolution is governed by the T-product between a third-order dynamic tensor and a third-order state tensor. In particular, we examine the data informativity of TPDSs concerning system identification, stability, controllability, and stabilizability and illustrate significant computational improvements over unfolding-based approaches by leveraging the unique properties of the T-product. The effectiveness of our framework is demonstrated through both synthetic and real-world examples.