The combined system formed by a dual-arm space manipulator and a captured space target exhibits complex characteristics such as high nonlinearity, high redundancy, and strong closed-chain constraints. The dual arms drive the space target through contact forces, which simultaneously disturb the base. This creates a coupled control challenge where contact force distribution affects base attitude stability, further leading to inaccuracy in position control of the space target. Existing studies often treat trajectory planning and force allocation as independent issues, which can easily overlook the strong constraints of closed-chain kinematics. To address this challenge, this paper extends the nonlinear model predictive control (NMPC) framework to these closed-chain combined systems. By leveraging NMPC's receding horizon prediction and nonlinear optimization capabilities, the proposed approach simultaneously resolves position control and force distribution for the combined system under closed-chain constraints within a unified optimization framework. Specifically, this paper first establishes the dynamic model of the combined system, then incorporates the closed-chain constraint equations as equality constraints in the nonlinear optimization, and designs an NMPC controller with state control and minimum energy consumption as the control objectives. Subsequently, the stability of the controller is proven based on the recursive feasibility of the initial solution and the monotonic decrease of the cost function. Numerical simulations demonstrate that the proposed method successfully achieves position control of the space target and optimal distribution of dual-arm contact forces while ensuring closed-chain constraints and maintaining the stability of the base attitude.