The bit at 2:50 is a standard 2-bar vamp in the key of A major. He is playing two chords to the bar like this:
/ A A#° / D6 E6 / He plays this vamp three times.
Then he does a little walk-down playing four chords to the bar like this:
/ E6 D#6 D6 D6 / ...and finishes with (maybe) one beat of Amin7 and three beats of E7 like this:
/ Am7 E7 E7 E7 / ...adds an extra measure of E7 while removing and replacing his index finger on the G-string
/ E7 / ...which is kind of strange because it breaks the 2-bar pattern from the stuff above.
The E7 serves as the turnaround back to the A chord, so he essentially made an extra bar of turnaround. He finishes by playing two measures of A, kinda alternating between A and Am7 by placing and removing the fingers off of the A-chord.
/ A / A /
A 2-bar vamp such as this would have been used in lots of tin pan alley type tunes, so that is why it sounds familiar. But I don't believe he is playing any particular tune because the extra measure of E7 is a little strange to me. I think he is just using shooting from the hip for a demo.
If you like the sound of the vamp, you should 'steal it' and work it into your own song. Nobody can copyright a chord progression, so steal away!
The rest of the faster strumming is 12-bar blues in A.