solenoid with a spring, integrate the voltage vs time per press,
the solenoid type looks to be about $3 per unit with a built in spring, so just need some buttons and a way to attach them
you could also create a fun self playing mode demo where the buttons pull themself down :p
or a hard mode, where certain actions in the game disable certain buttons for a few seconds by holding them down

Other possible way would be getting a PCB stencil for the fingers, fit them with small strain gauges and put springs under the end of the fingers, its more a measure of difflection, but with some math you can work it out.