I turned the photo on it's side so that you could more clearly see the S configuration there. The 2x the pipe diameter from the weir to the inlet is what makes a P trap a P trap. Where the trap vents from is incidental. That trap in that configuration will siphon just fine with or without that vent. I have set that exact same thing up in the lab many many times using clear 2" PVC and fittings. given enough velocity (which a washer has) it siphons every time. Increase the weir to inlet by 2x pipe diameter or more and it never siphons. I can't think of a single plumbing code that will allow that configuration and again, there's not a plumbing inspector either state or local that would let that go around here including me.