Noam Wallenberg sets up a parallel distortion chain on a snare to push it toward a deliberately exaggerated, cartoony punch instead of a clean boost.
He sends pre-fader so the chain keeps running even when the snare channel is muted, then gates it hard to grab only the hit itself, dialing in hold so the tail doesn't get chopped off.
A ping pong delay adds width before the distortion stage. He finds the sweet spot by ear, steering clear of roughly 9ms where it flanges and thins out, and 16ms where it starts to flam, landing on 13ms for a tight doubled sound.
The channel strip's drive stage is where the character actually comes from. From there he reins in an overblown fundamental, shaves off the super highs, and rolls off more top end on a final EQ before blending the distorted signal under the dry snare.