No, that video game runs on 6502 or similar CPU. It is possible to emulate NES using PIC, using various models, check this link as example:


For the my intended music playback, 877A uses DT-INTs, and for the easter egg moment, which will be achieved when user presses certain combo of keys, ther will be a small animation on 1602 display, and music should be playing, MCU won't be doing anything sophisticated that time.