Final answer:
The cytoskeleton is responsible for contractile movement in smooth muscle cells, primarily through the interaction of actin filaments with myosin.
Step-by-step explanation:
The organelle responsible for contractile movement in smooth muscle cells of eukaryotic organisms is the cytoskeleton. The cytoskeleton is composed of microfilaments, intermediate filaments, and microtubules. Actin filaments, which are a type of microfilament, work alongside myosin to facilitate the contraction of muscle cells. This well-studied interaction between actin and myosin is the basis of muscle contraction, including in smooth muscle cells where involuntary contractions are necessary for various body functions such as digestion and circulation. The process of muscle contraction in smooth muscle tissue does not exhibit the striations typically observed in skeletal muscle because the structure of smooth muscle is different, with actin and myosin arranged in a less orderly fashion.