Depending on the video format you will need the codecs to make sure you can play them. (K-lite codec pack is free and will cover most formats)
You will also need a media player that has a balance control for audio eg Winamp (free) and allows multiple instances so you can watch two vids simultaneously,Winamp again. (others will allow multiple but I'm not sure if they have an audio balance control)
Put the audio from one to the left and the other to the right.
Plug in headphones...Bazinga !
I have used this method myself, i'm sure theres other software out there to accomplish this but this is the only one I have used. Best of all its free !