An NFT owner is effectively an executive producer.
Film and television production has a credit known as "executive producer." Wikipedia's article about this role states that it includes financing the work and may include participating in its production. Especially in television, not every executive producer is a "showrunner" with creative control. As Nobby wrote in an answer about executive producers of America's Got Talent:
These days it is more common for people to 'buy' themselves a credit on TV and film productions through financial backing, sponsorship or other enabling methods.
Traditionally (at least on film), the executive producer(s) coughed up the money to get the production rolling - they generally wouldn't have any other impact on the production.
Someone who purchases a non-fungible token (NFT) from a work's author likewise financially supports the creation of a work by contributing an amount of cryptocurrency in exchange for being publicly credited as the work's NFT owner.
In a few cases, the author agrees to bundle other rights in a work with NFT ownership. This may include a license to commercially exploit a work, as in the case of Kevin Smith's 2021 film Killroy Was Here.