Thanks for asking! The videos about GiveWell should be about GiveWell itself (as an organization). And should solicit donations for the (evaluation) work of GiveWell. Then there should be no problem. If you (also) want to make a video for a GiveWell-recommended charity, you can make a video for the Against Malaria Foundation. :)
The video was made by EA Barcelona. Perhaps @Melanie Brennan can say more about that?