While it's not out of the ordinary to capture seahorse births on video in aquariums (just do a quick YouTube search), capturing one in the wild is more rare, according to UBC.

No, it’s not a pony like the famous wild horses of Assateague Island National Seashore. It’s a lined seahorse (Hippocampus erectus), the only species of seahorse, ...

Yes, meet the Hippocampus erectus. ... After a convulsive “birth,” during which the male seahorse’s body expels the contents of the pouch, tiny juvenile seahorses emerge.