You can record to any device that has a video-in and video-out connection of some kind, if the video-in is compatible with the game machine and the video-out is compatible with the television. People used to make these captures using VCRs, in the pre-PC days.
From there, it's a matter of finding a device that will record digitally and either a) is a computer, b) can transfer files to a computer or c) can upload to YouTube directly.