What is right wing about that process? The Democrats support the movie industry, not the Republicans.
The fact that Democrats support something doesn't negate the possibility of something being right wing. The Democrats are not ideologically pure, or ideologically homogenous, and very few of them can be considered "left".
To me, pretending that copyright is only about property rights, and ignoring the fact that copyright was also supposed to be about free speech and about making material available for free to the public after a limited time, is definitely "right wing".