There's a concise writeup of the technology here:
https://en.wikipedia.org/wiki/Zink_(printing)
Basically, they're heat-sensitive dyes that are colorless in the unprocessed material, but can be heat-activated and will then retain their color as colorful dyes afterwards. Much like in a color negative film, there's a yellow top layer, then magenta in-between and cyan at the bottom. The top layer responds to fast & intense heat pulses where as the cyan bottom layer responds to slow/long lower-heat pulses. Magenta is the middle ground.
I expect real-world resolution will be a little less than for an optically activated material (unless it relies heavily on chemical diffusion, as in the case of Polaroid & Instax). That's just a hypothetical guess though. I've never worked with this material.
And yes, the camera is really just a small digital camera (much like in a smartphone) packaged together with a small thermal printer. I guess (wild guess) that the printer uses piezoelectric technology to heat the pixel sites.
Pretty neat technology.