Display Screen with Animated Graphical User Interface of a Gaming Machine

FIG. 1 is a first image in a sequence for a display screen with animated graphical user interface of a gaming machine with growing effect showing our new design; FIG. 2 is a second image thereof; FIG. 3 is the third image thereof; and, FIG. 4 is the fourth image thereof. The appearance of the graphical user interface sequentially transitions between the images shown in FIGS. 1 - 4 . The process or period in which one image transitions to another forms no part of the claimed design. The peripheral broken line represents a boundary of the display screen with animated graphical user interface and forms no part of the claimed design. The broken lines depicting the remainder of the display screen with animated graphical user interface of a gaming machine form no part of the claimed design.