Another way to say conversion went from 0.5% to 1.3% is to say visitors were over 2.5 times more likely to convert if there was video than if there wasn't. In those terms, random fluctuations seem less likely as the reason for the difference.
Yes, but it's just because it sounds different. IMO both the absolute and relative number of people lay in a range of what I would expect to be random fluctuations.