This exercise is from the Core Skills section on Muting.
This is a typical funk chord sequence: E sus4 - E maj (repeat) and up 3 frets to play G maj - G sus4 (repeat). Followed by a weird jazzy one-finger barre progression for no particular reason.
You don't have to use your thumb to mute the lower 3 strings. Yet, using your thumb to mute will make things easier for your strumming hand.
If you do use the thumb to mute remember it is functioning only to deaden the strings from sounding out. So although we show the thumb muting at certain frets - don't feel you have to stick to that fret. As long as your thumb is muting the string and not accidentally sounding out harmonics, that's all you need do right.
As for the funk chord playing - remember it's all about rhythm. Use constant strumming, and mute the strings at rhythmic points to get that lovely 'clickity click' effect in between chord strikes. Mute by fretboard hand only - not strumming hand - for this piece. Remember, for the muting, just raise your fingers off the fretboard a little so that although you are still striking the strings they don't ring out - they go 'clickity click' instead.
Echo and delay used in the normal speed version to give that 'U2 intro' feel.