The Constitution specifically authorizes federal copyright laws. "To Promote the Progress of Science and Useful Arts, by securing for limited Times to Authors and Inventors the exclusive Right to their respective Writings and Discoveries."

There are many problems with copyright, but the ones a "constitutional originalist" should take issue with from that quote are that:

First, inventors and authors frequently aren't the ones who hold exclusive rights to their writings and discoveries under copyright law, as their rights are often signed over to others; and these rights are often continued to be held even after the authors and inventors die.

Second, there weren't any movies or videos or even recordings back when the US Constitution was written, so their writings couldn't possibly directly apply to these media.

It takes interpretation on the parts of these supposed "constitutional originalist" justices to decree that these new media do in fact fall under copyright law.

The current state of copyright law is far more a transgression against the bit about "securing for a limited Time" than against the 1st amendment.