Muting is the opposite of strength, actually. Just a gentle touch is all it takes. There are lots of ways you can mute, but you have to make it work for the song and within your individual technique.
Here’s the way I do it. I only worry about muting the top 3-4 strings: I just release the chord and keep the chord shape (except for typically touching the low E with my middle finger and I don’t stretch it out like Tony does in the video. That’s not working for me). Then I make sure not to hit the B or high E with my strum, because I’m not muting them. I’m only striking the top 2-3 strings.
I play the whole riff very loosey-goosey. I know they’re called power chords but when I don’t introduce a lot of strength, it’s been working way better for me.