An interesting approach would be to actually have one central Arduino connect to the game via Serial, and then have other Arduinos talk to the central Arduino via I2C. That would let you basically have as many Arduinos as you want in a game controller setup, but never have to worry about managing a lot of USB cables, etc.
One thing this would do is let you have the satellite Arduinos still connect to your PC via serial, but they would purposely NOT participate in the handshake procedure with the game. That would leave them free to output any kind of trace and debug messaging they wanted via Serial, without interfering with the game.
Another advantage is that you won’t have to worry about running out of I/O pins for interfacing, nor do you have to dedicate a whole Arduino to a very simple task. A little, cheap ATTINY85 based Arduino with just a handful of I/O pins could manage part of your control setup for example.
To make this all work, you’d basically want to modify the Arduino library so it would allow an alternate I2C-based handshake by satellite Arduinos with the central Arduino. The central one would handshake with the game, and then listen for handshake requests in turn via I2C from satellite Arduinos.
The Central Arduino would then just rebroadcast (via I2C) every single serial input it got from the game to the Satellite Arduinos. And in turn, the Satellite Arduinos would broadcast any game command they wanted to send via I2C, and the Central Arduino would simply echo their messages out the Serial port for the game.
If you’re not familiar with I2C and the idea of having two Arduino’s talk to each other with it, check out https://www.arduino.cc/en/Tutorial/MasterWriter for some background. An article at http://www.techbitar.com/how-to-network-many-arduinos-with-sensors-using-i2c.html shows how you can have multiple Arduinos involved.