You're trying to do multiple things here, and the tough question you have to answer is whether you want to do each of these things before or inside the computer. You want to:
mix the stereo signals of two gameboys
EQ each of the stereo signals separately
get the audio into your recording software
One at a time:
Mixing: If you mix the signals before the audio hits the computer, their relationship is permanent. If you record the two gameboys onto separate channels in multi-track recording software, you can adjust the mix freely.
EQ: same as mixing - the only downside is that if you do a bunch of live EQ work, then you will need to either buy a controller for your software to play the effects the same way, or simulate your EQ tweaks using automation.
Getting audio into your computer - you can survive by just running the output of a mixer (or straight from a gameboy) into the line or mic input on your computer, but it won't get you nearly as far as having some kind of proper A/D. You'll find that the input is easy to overload, the quality doesn't stand up to other recordings, and you may lose bass response that you won't be able to get back with EQ.
This interface can come in the form of a standalone device, or can be built into a mixer, although googling right now I can't find any models of USB mixer that output more than a single stereo signal - I know they're out there though.