Doubtful it's a full wave forward converter: that would require a FWB on the secondary, and screw that at those voltages and currents. It would be FWCT.
I was looking for the common ground lead in the second picture, but there it is, none to be found. So it's not FWCT!
Seems it's a new power supply. "ATX" covers a huge range of history by now. They used to be BJT half bridge inverter, forward converters. Then MOSFET, and now they seem to be largely 2-switch forward or flyback. The above seems to be the latter. Whether it's forward or flyback depends on the magnetizing inductance (high or low respectively), and whether the original application had a secondary series filter choke or not, obviously.
It's also consistent with an ATX supply in that there will be an aux supply for primary control power, optionally secondary control power, and motherboard standby. No need for an aux winding on the main power transformer, hence the sparse primary side pinout.
Active clamp flyback is also pretty popular, though I'm not sure how common it is among offline supplies, and it seems to give awful efficiency at light loads? At least that seems to be what I've observed from a few 1/nth-brick DC-DC modules I've seen.
The 2-switch configuration seems to be popular with active PFC, probably part of the motivation behind it; straight flyback or forward (half wave) would require very high voltages, making trouble with transistor selection, trace clearance and EMI. Half bridge should still be attractive though, with LLC resonant being an option; perhaps the reduced EMI of 2-switch is worth the change after all. (Or maybe it makes no difference because you just can't time the switches accurately enough to get balanced primary voltages.)
Tim