A control circuit of a master-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 master-side game console and a client-side game console; receiving master-side input values generated by an user control device of the master-side game console; receiving client-side input values transmitted from the client-side game console; generating a target instruction based on the master-side input values and the client-side input values; transmitting the target instruction and a pseudo clock indicator value to the client-side game console; executing the target instruction in a master-side emulating environment based on the pseudo clock indicator value; and rendering an updated master-side game screen according to execution results of the target instruction and displaying the updated master-side game screen on a display device.