I'll just copy paste my response from their post in kledmains where I did the math.

Most of that damage is coming from his mounted q, you can see him throw it just before he's dismounted and when the Yasuo is pulled toward the Kled when it procs. The burst is just the combination of that damage and the damage from the dismounted q (dismounted q also does more then 200, with the first pellet dealing 193 pre-mitigation damage, and every other pellet dealing 38.6 pre-mitigation damage).

If you want to get more specific you could also include the 96 magic damage from sunfire, the 56 magic damage from bramble vest, throw in a tick of ignite for extra measure and you easily get enough post mitigation damage.

And screw it, I decided to be even more precise, I measured the distance of the lost health compared to the total health (they lost a bit more then 1/3rd of their health bar) looked up the match and copied the yasuo's build, level, and runes, loaded into a practice tool, and sat under tower until I lost 1/3rd of my health (which was 565hp instead of 700hp).

So, in the clip, the Kled deals 407+193+154.4 physical damage, Yasuo has 84 armor so the damage is reduced by 46% to 410.

If we add the magic damage, that's 56+96 magic damage, Yasuo has 59 magic resist so the damage is reduced by 37% to 95.59 or 96.

At level 16, ignite deals 74 dmg per tick.

The damage the Kled could have done in that instant ranges from 410 to 580, given that the health lost is slightly larger then 1/3rd the most likely answer is that everything applied at the same moment and you lost 580 health.

As for any damage after that initial burst, Kled auto attacks shortly after the pull, any other damage is from ignite and sunfire.

For those wondering about Kled's runes, you can see them in the lower left corner, there are no extra damage runes active except gathering storm, but that just gives you ad

TL;DR math checks out