Player character's arm is actually a cannon/gun, or can wield a gun that envelopes the hand/forearm or is mounted on the arm (e.g. wrist gun).
Alternate name: Arm guns
The first video game about Arm cannons was released on August 6, 1986.
Oldest example of any kind of arm cannon is possibly in Cyborg 009 (1964), and possibly oldest example of non-robot/mecha having such is in Cobra (1978). Neither are confirmed as earliest of either for now, as digging up examples of this is difficult at best.