One of the tricks to playing a tune like this is to dig in. As you can see in the video, I'm hitting the strings very hard which is a part of the sound of the music. Hitting the strings like that not only overdrives the amplifier but also creates a certain envelope to the notes that sounds awesome!
Oddly enough, playing aggressively like that certainly makes the music sound much more aggressive, who would have thought? ;-) Joking aside, it takes a lot of practice to play that aggressively while keeping the lick clean and in time. My suggestion is to learn the song picking normally to make sure you have the notes, then start to really dig in and get into the groove. Another example of a great riff that is played hard is Led Zeppelin's "Black Dog"—we can really hear Jimmy page hitting those strings hard on that tune, and we want to do the same here. As usual, definitely listen to "Evil" by Cactus.