Well the G620 in and of itself, is not a bad chip
It just doesn't handle graphics the same way.
I do believe you should be able to play 1080p video without any real problems though.
So maybe we should look a little more closely at that problem.
Does it happen no matter what player you use?
Here's a good free one that doesn't rely on windows codecs for video playback, so I often recommend it for troubleshooting things like this. (and who knows you might wind up liking it.) VideoLAN - Official page for VLC media player, the Open Source video framework!
If you play the video through it do you get the same problem?
Do let it play for a few minutes.