The core ought to be engaged in any type of movement. This is where movement originates from.
It is important to remember what the core is. The core is all the muscles that are attached to the axial skeleton and dynamic movement involves large rhythmic movements that involve not only the muscles of the core but muscles involved in the activity to be performed.
The short answer is “yes,” the core is definitely engaged in dynamic warm-up movements. The general focus of dynamic warm-up is to increase the ROM and internal temperature to prepare us for the activity to come. Most dynamic warm-up involves the large muscles of the body and thus the core. Since dynamic warm-up requires movement, and most movement involves (generally speaking) the core, the answer is yes (at least in most instances).