This is where things get fuzzy, and probably the only people who truly know are the copyright lawyers who've read the original contract. I know there's a law where screenwriters who create original material are allowed to take back partial ownership of the work after 35 years, and that there was a spree not too long ago of writers of hit 80s movies doing just that. There's also the aspect that Friday the 13th was originally an independent film that was purchased by Paramount rather than something the studio made themselves, which opens up the question of what rights they originally bought.
Either way though, New Line owns the trademark (unlike Evil Dead, where the trademark is owned by Renaissance Pictures) and Jason Universe is clearly able to do stuff outside of their remit.