In this paper, we simply derive matrix inequality conditions on the terminal weighting matrices for linear discrete time-varying systems that guarantee non-increasing and non-decreasing monotonicities of the saddle-point value of a dynamic game. We show that the derived terminal inequality conditions ensure the closed-loop stability of the receding horizon H-infinity control (RHHC). The stabilizing RHHC guarantees the H-infinity norm bound of the closed-loop system. The derived terminal inequality conditions include most well-known existing terminal conditions for the closed-loop stability as special cases. The condition on the state weighting matrix is weakened so as to include even the zero matrix. The results for time-invariant systems are obtained correspondingly from those in the time-varying case.