Here is what I think he is doing.
Tuning is a hybrid: E A D F# A D
Play the G chord as 3 X 5 5 5 5
Play the Am as 5 X 5 6 7 7
Play the C chord as 8 X 10 10 10 10
It feels odd at first, and because he has the long 4 jointed thumb, he can play the bass notes wrap around
which is very difficult for me. But after playing it a few times, it gets easier.
"Play the Am as 5 X 5 6 7 7"
Wouldn't the 5th string, 5th fret make it Am
7?
A x G C E A
Except for the 6th string, it is an open D tuning. If you tuned the 6th string to D, you could play the major chords by barring across all 6 strings. Of course you wouldn't have to play all 6. The thumb over the top technique would probably still work and could mute the 5th string. The Am7 could be played:
X 0 5 6 7 7
and the thumb over top could mute the 6th string.On the other hand, with the original tuning, the Am7 is a movable shape and could also be used for Bm7, Em7 etc.
In the original tuning, if you wanted Am without the 7, there might be a way to finger this: 5 X 7 6 7 7