Yes, it all eventually becomes heat, though not all in the room. Some sound escapes, and some light goes through the window or whatever. Those losses are incredibly minor though.

What makes a big difference between a PC and something purpose built as a heater is generally how the air circulates the room. A space heater is going to project it out into the room, baseboard heaters will create a wide convection current. A PC on a desk in the corner will typically just blast hot air at one localised spot on the wall which isn't really ideal for dispersing it throughout the room.