If they’re not trying to produce something worth selling or publishing (as advertising), the motive is presumably to have something on file in case they have too many applicants to remember who’s who and/or to show people higher up who need to sign off on hiring decisions.
It’s still questionable though. If they aren’t willing to sign a contract regarding the recording (separate from the hypothetical employment contract to follow), what guarantee do you have that they won’t use the recording for any other purpose, like advertising on some social media channel you’re unlikely to notice, or (intentionally or unintentionally) sharing it with some opaque entity that will analyze it in furtherance of the development of teacherbots? Even with a contract, if that happens without your knowledge, you won’t be able to claim compensation.
If they absolutely need to let the fuzeren see your demo, they can invite the fuzeren to sit and watch it live.