So D1 must be a Schottky diode? By rectifying just one leg of the AC voltage you loose the isolation effect required to make AC and it becomes high voltage DC? Or, does D2 work with D1 to essentially make a complete bridge rectifier?
So this isn’t a SMPS is it? It’s just a linear PS with a rudimentary feedback protection circuit. Still, it looks familiar … like the “hot ground” on the left side of the transformer. If there was a chassis and chassis ground, it would only apply the left side of the transformer (low voltage side), right?
D1 is probably a standard 1N4007 or similar. It's just half-wave rectifying the AC in... with a large enough cap you will end up with a usable HV DC (HV bulk, Vrec, whatever you wish to call it.) Though your power factor is going to be horrendous since the input current waveform will have huge spikes each cycle, worse than using a full bridge. D2 is part of a snubber to protect the switch (Q1), nothing to do with the AC input.
It's definitely looking like an SMPS to me. They've just managed to use discretes instead of an IC to control it. (All in the name of saving those few cents!) The RC on the base of the switcher is being fed by the aux coil (once it starts up, thanks to the 1M pull up) which is turning the transistor on/off at some unknown frequency (probably 60-100kHz I'd guess.) The aux coil outputs the same waveform as the primary, and secondary (which would be 180 out of phase), It's chopped up DC, just at a different voltage. The primary is being connected/disconnect from ground each cycle, so it can do it's inductorly duties and get the flyback in the secondary going. But hell, I may be comepletely wrong about how that whole section works... I've only had experience with supplies with an actual controller IC.
The fabled "short circuit protection" is supposed to be Q2, sensing the current through R2 (and hence the primary) which is supposed to stop the switching if there's an over current problem. But like I said before, if an over current condition will smoke R3, well now you have no way of stopping the switch before it detonates.
Q2 looks like it may even be some type of duty cycle control for Q1, which would make sense, so that you can control the output. Who knows.
Still no idea how this passed UL.
Edit: Oh yeah, I never did ask... what is the output voltage/current? If it's low enough, having a horrible power factor may not be an issue. (So they're using a 2.2uF bulk cap? the PF might not be all that bad to begin with.)