You can use quick sync, but it isn't going to be as pretty as x264, but if you're going for viewable you should be fine. If you are going for very pretty then get a capture card like the elgato.
I got to say it's the screen that is probably the biggest feature I like about the G550JK. A lot of laptops in the similar price range might have very similar specs, but the screen tends to be bad and they should feel bad.