<p>This paper considers a class of stochastic nonzero-sum discrete-time dynamic games with networked players where each player has its own state dynamics which has the states of other players also entering with, however, some time delay. This <i>delayed coupling</i> makes this a nonstandard class of games where the existing theory does not apply, particularly since the underlying information structure restricts the players to use only their local states in constructing their controls. What is sought is Nash equilibrium under such information structure when there is a high population of players. The paper introduces a general methodology within the <i>mean-field framework</i>, and applies it to games with linear dynamics and quadratic objective functions for some explicit characterization of the <i>mean-field equilibrium</i>, which is then used to obtain an approximate Nash equilibrium when there is a finite number of players. The approximate Nash equilibrium policies of the players turn out to be in the form of current local state feedback and some mean-field term generated by high-order dynamics.</p>