But taking something without paying for it is not always theft; and one could imagine thieves paying a token amount for something in order to claim it is not theft.

Most importantly, copyright infringement, unlicensed use, and piracy usually fall into the category of "IP theft," which differs from real theft of physical property in important ways such as the harm caused to the owner (e.g. potential lost sales or licensing revenue vs. losing a physical item) as well as associated penalties and remedies.

> In the case of games, music, etc, you don’t pay for the file itself but for the work the artist put into it.

You're paying for the file and the rights to use it.