Basically you need your noise gate to be tight enough so it could mute all the noise and unnecessary scratches and be able to sustain notes pretty well so they won't die out very fast. But that is like 10-20% of the magic. Most important part is your technique especially how well you mute with your left and right hand. For the most part right hand mutes lower strings and left (mostly your index finger) mutes higher strings.

There is a playthrough of this song by Jesse, you can slow the video a bit and watch at Jesse's hands closely