Windows software for recording multiple video/audio sources?
If it were me, I would try using a video recording interface with RCA connectors, as most TVs have an RCA audio/video output. Most of these connect via USB and come with some sort of software. For the video of the players, use a second software program and webcam/etc. to capture this. If you had a Mac, this could probably be sync'd in Final Cut Pro. I'm not familiar with all the software for Windows. 

The main part I don't think you'll be able to accomplish (without expensive software) is capturing all of this in-sync with each device. This would require some sort of video-switcher software, similar to what TV stations use for live broadcasts. The method above is probably your cheapest route, if you can handle syncing it after the fact.