The parkour down/controlled descent mechanic was first advertised as a brand new addition to the movement system in Assassin's Creed Unity. However, what most players don't know is that a version of the mechanic called vaulting was present in the series as far back as the first game, Assassin's Creed. This mechanic is never tutorialized by the game and requires specific contexts in order to be possible.

To perform a vault in the general case, Altair must perform at least two jumps in a row and must hold down empty hand as well as HP, forward and legs during the final jump the player wishes to execute a vault on. A special case where Altair is already perched on a non-standing surface allows the player to vault without requiring an initial set-up jump.

An additional mechanic utilized in this video are the roof dents in Damascus's poor district. Running off of these dents in the roofs in HP will allow Altair to smoothly parkour down to street level without taking damage.

Special thanks to Leo K for teaching me how to perform this move via this tutorial (   • [Rogue Academy] AC1 | Vaulting  ) and for inspiring me to make this video from a comment he published under that video.