How do you plan on storing all this data and what format? Have you got the hardware interface designed, if so post a schematic, not a frizzy thing. I am not surprised you could not find it, something like this takes a lot of time and resources. Validating it will be a real interesting project if the game used random numbers.
In theory this shouldn't be too hard. What you're describing is essentially a keylogger.
Do you know what signalling the controller uses?
If it's one wire per button then it should be fairly straightforward. Connect each of the gamepad button pins to an Arduino input pin. Connect an Arduino output pin to each of the corresponding console input pins. Use the Bounce2 library to determine if a button has gone high or low. If so, set the Arduino output pin to match it Then save the number of millis() that have elapsed since the timer began to the SD card.
Your SD card will end up with a file that looks like this
Time.. Button.. Button state
0..... Left.... HIGH
234... Up...... HIGH
1257.. Left.... LOW
5347.. Up...... LOW
The entire loop that checks to see if a button has changed state will be pretty quick, probably less than a millisecond. Writing to the SD card will be relatively slow so you may want to hold 200 or so button events in RAM before writing them to the card all in one go.