YouTube's 60fps runs smoother than games?
If you're comparing PC games to Youtube video shot with a camera (as opposed to Youtube video of games captured via HDMI), then you're probably noticing the natural motion blur that cameras introduce.  Gaming hardware can't reproduce this effect very well because it either has to render intermediate frames and blur them together or perform "optical flow" or vector-based analysis in real time.

If you are, however, asking about Youtube videos of video games (which presently comprise most of Youtube's 60p content), then my only suggestion is perhaps a performance difference between your machine and the ones in the videos.