I work in social, including for some equine NGBs and horse shows. The FEI will not monitor everyone’s social, absolutely no one has the time.
This doesn’t indicate that filming is banned overall, just that “capturing video… and posting at a later date is forbidden.” So you’re welcome to film all you want for your personal archives, but the FEI can claim copyright if those videos become public.
To me, this reads as primarily intended to protect whoever has paid for the broadcasting rights to the event, with the bonus that if a “non rights holder” DOES video & post something the FEI doesn’t want on social, and it causes a fuss, the FEI can issue a copyright strike and the social media platform hosting it will take it down. The FEI can also copyright strike any creative “edits” of their publicly posted footage.
I do not think that videoing your own horse and texting it to a few people violates this policy. Ripping your horses’ round from fei.tv or FEI social and posting it on your website or Facebook does - because the FEI wants to be sure they or the broadcaster are paid for your commercial use of that footage. And they want the legal right to get a shady video of a horse with a blue tongue at an FEI event taken off social before it goes viral.