The ornamental design for handle base for game controller, as shown and described.
FIG. 1 is bottom perspective view of the handle base for game controller of the invention.
FIG. 2. is a top view thereof.
FIG. 3 is a right side view thereof.
FIG. 4 is a bottom view thereof.
FIG. 5 is a front view thereof; and,
FIG. 6 is a rear view thereof.
The left side view of the handle base for game controller of the invention (not shown), is a mirror image of the right side view shown in FIG. 3. Portions of the controller shown in broken lines form no part of the claimed design.