Fraps records in .avi and is pretty much lossless, so yes the original videos are going to be incredibly large, and yes you can make the videos smaller, but still retain HD quality. An easy way to be to simply use Windows Movie Maker. Load your .avi file in, and then promptly save the movie, but choose the 'Custom' Setting at the very bottom of all the quality pre-sets. Set the resolution to 1920x1080, the FPS to 30 , asYoutube only displays 30, so anything higher will just increase size. This is also the reason the file you got back was smaller, because the framerate had been capped. And finally, change the bitrate to something manageable for gameplay like 15000 kbps.
1920
1080
30 FPS
15000 kbps
The settings I normally use^