Are you sure that the 3rd is omitted? It's really rare to omit the 3rd, because it really signifies the quality of the chord (major or minor). Usually, when people want to omit a note in a 7th chord, they omit the 5th.
A maj7th chord without the third, would be a power chord with a maj 7th (?). What I mean is that it could be both a major chord with a major 7th and a minor chord with a major 7th, and you wouldn't know which one.
From what I've seen on guitar, they omit the 5th or none at all
Εdit: From your image, I can see that he is playing twice the 5th (D). One time as an open string, and one as the 3rd fret on the B string. I don't see any point in doubling the 5th and omitting the 3rd, when you can play both, simply by playing the B string open (which is the 3rd of the chord).
This seems wrong to me.
Here is a way you can play it, without omitting any note:
And I've also found some other ways to play the chord: