Neopomacentrus filamentosus is an egg-laying species. The male fish in this video appears to be establishing a territory. It does so by cleaning a rocky ledge or coral surface. The male fish will court the female and encourage her to swim to the cleaned spot. During the actual spawning, the female will deposit her eggs and they will be promptly fertilized by the male. Courtship and spawning will typically take less than 20 minutes. Each female can deposit up to 20,000 tiny eggs per spawning. Some species of damselfish may breed with several females, while others form distinct pairs during breeding.
At 1:05 another fish enters the territory. I suspect that this might be a female as the male does not chase it away. It fact, the male seems to hang back to allow the fish to enter the territory. And when I played it in slow motion, the fish that enters the territory appears to graze the surface with its anal fins before it exits.
After spawning, the male will guard the spawning site and tend to the eggs. He will use his fins to aerate the eggs by fanning fresh water over the eggs; he will also remove any eggs that fail to develop. During the breeding period, the male will tirelessly defend the eggs and territory, even against fishes that are much larger than him. The eggs are demersal and will typically hatch after 3-7 days and the tiny fry will feed on plankton.
I’ve identified this damselfish as the Brown demoiselle (Neopomacentrus filamentosus), but I may be wrong. Please contact me if you think it might be something else.