Realizing versatile and human-like performance in high-demand sports like badminton remains a formidable challenge for humanoid robotics. Unlike standard locomotion or static manipulation, this task demands a seamless integration of explosive whole-body coordination and precise, timing-critical interception. While recent advances have achieved lifelike motion mimicry, bridging the gap between kinematic imitation and functional, physics-aware striking without compromising stylistic naturalness is non-trivial. To address this, we propose Imitation-to-Interaction, a progressive reinforcement learning framework designed to evolve a robot from a "mimic" to a capable "striker." Our approach establishes a robust motor prior from human data, distills it into a compact, model-based state representation, and stabilizes dynamics via adversarial priors. Crucially, to overcome the sparsity of expert demonstrations, we introduce a manifold expansion strategy that generalizes discrete strike points into a dense interaction volume. We validate our framework through the mastery of diverse skills, including lifts and drop shots, in simulation. Furthermore, we demonstrate the first zero-shot sim-to-real transfer of anthropomorphic badminton skills to a humanoid robot, successfully replicating the kinetic elegance and functional precision of human athletes in the physical world.