In this paper, we revisit the scenario that an internal gradual magnetic dissipation takes place within the wind from a newborn millisecond magnetar can be responsible for gamma-ray burst production. We show that a combination of two emission components in this model, i.e., the photospheric emission from the wind and the synchrotron radiation within the magnetic reconnection region, can give a reasonable fit to the observed spectrum of the prompt emission phase of GRB 160804A. We obtain the physical parameters through a Monte Carlo procedure and deduce the initial spin period and magnetic field of the central magnetar. Furthermore, the independent afterglow fitting analysis gives a consistent result, adding great credibility to this scenario. In addition, we predict a subclass of GRBs called bursts from such a Magnetar wind Internal Gradual MAgnetic Dissipation (abbreviated as MIGMAD bursts) that have several distinctive properties.