Seems like the others got you covered with the recommendation of Mirror's Edge Catalyst, so I'll take the opportunity to recommend something else a little similar to what you're looking for. One of the best systems of parkour I've seen is in Dying Light, pretty chill game on the lower difficulties but if you pump it up to nightmare it's one of the best horror/zombie games in a long time IMO, parkour is super solid and I like the way it's implemented in the game, since rather than making situations where you're forced to parkour, the game just plops down zombies everywhere and makes parkour your only safe way of avoiding them, and you get so easily overwhelmed that parkour just becomes second nature for getting anywhere. Sequel is being worked on as well, and shouldn't be too far away, so that's sick too! More on reddit.com

If there was a game that emphasized Parkour mainly for exploration with little to no fighting would be great. Unlock wall runs or leap further. More on reddit.com

Usually people seem to say the parkour is the best part of dl2. Only kinda complaint I remember having about it was from the world design being too repetitive and maybe some animation locking, from things like the slide which feel pretty slow to perform. The skills are also pretty lacking, having so many repetitive ones really killed my motivation to max level my parkour. But the parkour system itself seems to be the most popular part of dl2. More on reddit.com

Mirror's Edge is the parkour game. In most situations you're supposed to escape rather than shoot (you don't always have a gun, only temporarily when you disarm someone) but it still might be of interest. More on reddit.com