The integration of embodied intelligence into physical environments marks a new frontier in the evolution of intelligent systems. While the Internet of Things (IoT) connects devices and Artificial Intelligence of Things (AIoT) embeds intelligence into them, we argue that a further conceptual leap is required—one that enables the composition of intelligence itself through real-world embodiment, interaction, and evolution. We introduce the paradigm of Embodied Intelligence of Things (EIoT) as a foundational framework for distributed, physically grounded intelligent systems. EIoT systems are structured across three essential dimensions: Enacted, where devices are transformed into embodied agents; Engaged, where agents interact opportunistically based on physical and contextual constraints; and Evolutionary, where intelligence adapts and self-organizes through continuous experience. We further outline a developmental trajectory for EIoT based on the openness of perception and decision spaces, providing a conceptual map from tightly constrained agents to fully autonomous and adaptive systems. This work aims to establish EIoT as a core architectural and theoretical direction for future embodied intelligent systems.