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It seems to be a Tandy 1000 RSX which supports Windows 3.1

Original photo is from here, which has Windows 3.1 running: http://www.oldskool.org/guides/tvdog/RLRLX.html

It's a 386SX, which absolutely will run Windows 3.1 but if you're going to be real picky, it definitely won't be as snappy as in the video ;)

Question is, would you be able to put a Soundblaster 16 inside it?

Tandy 3-voice can play midi without an add on card.

Right but I know Yamaha OPL sound when I hear it.

The Tandy 1000 RSX has several ISA expansion slots. Putting a Sound Blaster in it is no problem.