A control circuit of a client-side game console includes: a processor and a storage circuit for storing a computer program product. The processor is arranged to operably execute the computer program product to perform following operations: establishing networking connection between the client-side game console and a master-side game console; receiving client-side input values generated by a user control device of the client-side game console; transmitting the client-side input values to the master-side game console; receiving a target instruction and a pseudo clock indicator value transmitted from the mater-side game console; executing the target instruction in a client-side emulating environment based on the pseudo clock indicator value; and rendering an updated client-side game screen according to execution results of the target instruction and displaying the updated client-side game screen on a display device.