Like an AR-15 lower, with a tommy upper. But everything is backwards. The counter and charging handle should be on the right side of the gun - unless he built it for a lefty. But did they ever make a left-handed version of the Thompson? Or maybe the video is just flipped. But then I don't know if the ARs had a select-fire switch on both sides, either.
(I'm not expert on real guns by any stretch, but have seen my share of Pulse Rifles.)
It definitely looks like an AR or M-16/M-4 lower.
I don't know what the heck the upper actually is (it actually looks like a toy I've seen recently), but I do know it isn't a Thompson.
The only variation of the Thompson with the charging handle NOT on the right side was the M1928, which had the handle on the top.
Far as I know the ARs only have select fire switches on the left side.
I'd be very interested to know what the upper receiver (and barrel section) is.
Kevin