The prevalence of ineffective corrective surgeries for ocular motor disorders calls for a robotic eye platform in aiding ophthalmologists to better understand the biomechanisms of human eye movement. This letter presents the first hardware design and implementation of a 2-DOF robotic eye driven by super-coiled polymer (SCP) artificial muscles. While our previous work designed and simulated a deep deterministic policy gradient (DDPG) learning-based controller that requires full-state feedback of the SCP-driven robotic eye, measuring the temperature states of the slender SCPs is generally impractical for the ubiquitously aimed robot. To address this predicament, this letter proposes a reduced-order state observer to estimate the temperature of SCPs given the kinematic measurements. Combining the designed observer and the learning-based controller, the closed-loop output feedback control is implemented on the robotic eye prototype to examine its performance on three classical types of eye movements: visual fixation, saccadic pursuit, and smooth pursuit. The experimental results are presented which successfully validate the observer-based output control of the SCP-driven robotic eye.