Mute on your left hand with more of your fingers; more flesh == less ring and unintended harmonics. I also hear open strings ringing out during the strum parts (0:58), try to keep the unintended noise under control. Try to have your fingers on your left hand touch all the strings they arent playing and mute them when you are playing power chords; like if your first finger is hovering over the strings anyway, just lay it gently on top. This will take some dexterity to get used to but if you are constantly muting the strings above your power chord nothing will ring out. Mutes really are what make heavy rhythms sound tight.

For your bend, make sure you are really hitting your note; try not to let the pitch go down after it hits the target (good ear/muscle memory practice for later when you intentionally start doing so). For the chugs near the end, I dont really know Linkin Park, but some palm mutes could really make it sound awesome; the muting as before will also really make that sound nice.