As a natural generalization of the Online Convex Optimization (OCO), Online Saddle Point Optimization (OSPO) involves a sequence of two-player time-varying convex-concave games. Instead of the duality gap used in most convex-concave optimizations, we choose dynamic Nash equilibrium regret (NE-regret) as the performance metric. We demonstrate that the implicit updates used to address OCO with dynamic regret can be extended to solve OSPO with NE-regret. To this end, we design two algorithms, the implicit online mirror descent-ascent and its optimistic variant. Analysis shows that their NE-regrets have the same expression form as the corresponding dynamic regrets of implicit updates in OCO. Empirical results further validate the effectiveness of our algorithms.