BOTRK on zed?

The only reason i know is that the active 10% of current health with his ult adds more instant burst damage and some additional speed in tight spots besides that no idea.

I think its the movement speed active.

I think it's the active they want. A not-insignificant addition to their burst damage, a small heal, and a movespeed drain to help ensure both that triple Q can hit and that Zed can get away clean.

The active for his ult and the attack speed helps him splitpush

It used to be pretty core on him, old guides will tell them to build it

Because his death mark deals damage the more you dealt within the given time window.

So if you ult a 50% HP target and auto attack him once, procing his 10% (iirc) max hp chunck passive, + Bork's 6% current hp passive and use the active on that target, thats another +10% current hp, not to mention the damage you ditch from your abilities and other auto attacks + Dusk blade proc if you time it correctly.

I can see it being super effective vs tanky champions.

The Active is really good for adding to his burst and sticking to champions who he can kill without using his ult (Yomuus + BOTRK active and autos given him a lot of movement speed and attack speed). The percent health damage on autos helps him with dueling tanks if he needs to fight them, and attack speed just feels really good on him.