When I started to watch this video I thought "oh, that's funny, a failed missile launch." Obviously, it didn't fail at all. That's exactly how the nuclear-capable anti-submarine missile RPK-2 Viyuga is launched: Just throw it in the water and it will come alive to deliver its warhead up to 28 miles away.
...it is designed to be fired from a 533 millimeter (21 inch) torpedo tube. It is boosted by a choice of mechanisms depending on model before clearing the water, firing a solid fuel rocket and delivering its payload up to 45 kilometer (28 miles) away. The payload ranges from a simple depth charge to a 200 kt nuclear warhead.
Both submarine- and surface-launched versions exist. The surface-launched versions are used by the Slava, Kirov, Neustrashimyy and Udaloy classes. The submarine-launched versions are used by the Akula, Oscar, Typhoon, Delta, Kilo, and Borei classes. However, the munition package used in either is identical and hence the ship-launched version is launched into the water and submerges before firing its engines.
In the case of this video, it's being launched from a Russian Navy's Udaloy II-class destroyer.