I have a few comments with the above circuit.
#1. The nor gates used have too many inputs. You can do the same circuit with a 3-input NOR gate.
#2. Since there is only one buzzer, this circuit is almost unnecessary. All you need to do is put any number of keys together (depending on # of players) in parallel. Connect it to +ve and the SET pin on the 4013 chip.
Connect the SET pin to -ve through a 1K resistor.
Connect Q to the output (buzzer or LED), then to ground.
Connect the clock to ground.
Connect data to ground.
now connect RESET to a key (which turns the output off), then to +ve. Connect RESET to -ve through a 1K resistor.
The buzzer will (and should) work now.