The "P" in "Model 4P" stood for "portable" — it was a modified Model 4 that was shrunk down to something roughly the size of a sewing machine. It had a handle on the back. Tandy's advertisements proudly proclaimed that it fit in overhead bins on airplanes. I feel sorry for anyone who actually tried that.
As far as specs, the 4P had a 4 MHz Z-80, a minimum of 64 kB of RAM, one or two single-sided double-density (SSDD) 5.25" floppy drives, and an 80x24 text mode. There was an optional 640x200 monochrome graphics card, but it doesn't look like this demo is using that. (I'd bet it's using the graphics characters in the Model 4's 80x24 text mode — faster and less data to deal with.) If I'm remembering correctly, the SSDD disks held ~180 kB, so there's less than half a megabyte of data in play for this demo. I'm kind of amazed at the sound in this demo — I'd never heard the speaker in my 4P ever make any noises other than simple beeps.
Semi-related trivia: The "best" word processor for the Model 4, SuperSCRIPSIT, was laid out on its program disk in such a way that the drive head's stepper motor played something that almost sounded like a song when it was loading itself off of the disk. Even ~30 years later, I can still hear SuperSCRIPSIT's loading sound in my head...