How does a joint need to operate and be structured in order to allow a person to do leaps of 10 meters in length with ease and without taking a long run first? Here's an example of what I'm talking about, the kid jumps around but it doesn't look like those movements are guided by muscle but by pure tendon elasticity.
Let's do the maths
Assume that the start and finish points of the jump are at the same height and the athlete's initial "launch angle" is close to the optimum 45 degrees from vertical. In that case a 10m broad jump requires that the athlete leaps with a velocity of around 11 metres per second and is in the air for around 1.3 seconds (to two significant figures).
If a 1.7m tall adult crouched down so their buttocks were touching their thighs then straightened up (including flexing their feet), their hips would move a total of about 50cm. (Source: Measurement of a person who crouched down and straightened up.) So that is the maximum distance that the acceleration can occur over. Plugging in the numbers, going from zero to 11 metres per second over 0.5m requires an acceleration of 121 metres per second squared, or about 12G for an eleventh of a second. This is roughly equivalent to the forces experienced by a person who steps off the roof of a two-storey building and lands on their feet without rolling. As noted by Soan, this force would be experienced on both takeoff and landing.
However, looking at the video clip in the example, the manga athletes were much less than 1.7m tall and were generally only bending their knees slightly. At a guess I would estimate that the hip displacement from "starting to jump" to "acceleration complete" was 20cm at most, which would require acceleration of about 30G. For comparison, the world record broad jumper mentioned by Chasly from UK would require an acceleration of about 3G.
Now we have the numbers, what does it mean? Firstly, humans simply cannot jump the way the manga athletes do, as it literally requires an order of magnitude more acceleration than elite human athletes can achieve. This xkcd What If question looks at a related question, with a similar conclusion. Even assuming cybernetic or genetic modification and enhancement of the bones, muscles, ligaments and tendons, the acceleration required would displace internal organs. Holding the spine rigid directly along the axis of acceleration will cause compression and injuries (assuming it does not separate from the pelvic structure altogether), while holding it at any other angle will result in a broken neck. The acceleration will bounce the brain against the skull, resulting in a concussion (at least) on each leap and landing.
However, just for a moment let us assume that the person (or manga humanoid robot, perhaps) both has sufficient power to make the jump and to durability to survive it. Looking at the example video, at about 2:30 a character finishes a series of leaps and then slides along the ground for several metres. Hmmm, let's think about that - it stands to reason that when landing with that much horizontal speed the friction of shoes against the ground is not going to result in an instant stop. But then... how was there enough friction to jump in the first place without the manga athlete's feet just sliding out from under them? Simply put, friction would not be sufficient - if the total acceleration is 30G, the horizontal component is going to be about 21G. Even spiked athletic shoes will not help (the spikes would break off), the only way to make a horizontal leap like this would require that both feet were braced against a solid object sticking up out of the ground.
In conclusion, it is not possible to have a human make jumps like this without having literally explosive joints to launch them (once) on a trajectory of that nature. While big cats do make very long jumps, with the best doing a standing long jump of around the 10m specified, this is possible because a cat is jumping with its entire body, flexing its spine and hind legs far more than a human can.
We humans already have the capability to do jumps like in your example. At least when electrocuted the reason our body doesn't let us is because this behavior can cause severe damage to our tissue when done repeatedly or sometimes even when done once.
So your real problem is how to change the body to be able to withstand huge jumps and strong acceleration/deceleration.
The biggest problem here is that our blood will simply leave your brain when jumping as the blood doesn't immediately accelerate with the rest of your body which would lead to a blackout when jumping too high or far (although it should be better when jumping far)
Your person has way less bendable veins and because your blood is mostly water it cant be compressed and as such has to accelerate with your body.
Or your Person has way more blood inside of it and there is simply no way to flow out of your brain for the blood.
The other Problem is how to keep your bones from breaking and your tissue from ripping from huge jumps, now one time jumps will not be a problem here because its the repeated stress which your body can't handle in this part. Landing shouldn't be a problem when the person simply does a roll as with this people parkour can already withstand drops from the heights shown in your example. The problem is the starting to jump because you can only go to the ground and cant increase the time to accelerate by much.
I do not possess a large amount of knowledge in biology so for this problem the only thing I can give you is to look at cats because they can jump quite high for their size.
It's been done. Spring-Heeled-Jack did it routinely to evade capture in the 1800's. Cape optional.
As you can see this is a pretty high wall. Picture is from the linked wikipedia page.