Okay, let's have a quick talk about "normal" Sins.
Normal Sins usually weave blindly aa-skill-aa-skill-aa-skill and so on, regardless of the skill they use.
This means they use an autohit, press a skill and then literally sit there and wait for the next autohit timer, to follow up with the next skill.
You can do that if you are a dual wielding Gladiator, since Gladiator's skills have really long animations (except for maybe the Body Smash chain or Sure Strike in later patches),
but the Assassin has many skills with very short animations, which allows you to spam two skills while still getting the following autohit timer, without any loss.
This results in more skills used in the same period of time and thus, more damage than usual.
If we take a look at the screenshots, we'll realize that the Sin is doing exactly that.
He's pairing Encircling Strike and Rune Carve during his burst on Pashid.
Also Fang Strike + Beast Kick (very short animations),
Assassination + Killing Spree and 2x Killing Spree (which are basically exactly the same),
then the single Rune Carve is a misplay (the only one I've seen tbh),
followed by Fang Strike + Beast Kick again.
And so on. You get the point.
If I say "any Sin can perform like that", I mean any Sin that wants to. Most Aion players are just lazy and ignorant though.
PS: I'm not playing Sin, so I can't help you out directly, but Para has already offered himself as a test subject and I'm sure he'd be able to perform well enough, so hf.