First off, you don't want a splitter, what you want is a "ducker".
I use em doing audio for corporate events where there are more than one speaker on the stage and one of them is working as a moderator or such. What they do is interrupt a specified signal when another is active. Like a side chain compressor. Probably too much for a game setup.
What I do is use a small mixer in my rig. Not only can I listen to any input or combination thereof but if the phone rings or I need to pay attention to another source, all I do is throw done a fader. It also helps getting the various input volumes under control. I also use a crossover to send lfo to a sub. That along with a bit of verb and dogfights take on a whole new character.