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.
Thou dost protest too much. You are trying to justify the unjustifyible. You could not make that trap siphon even if you put a suction pump on the bottom of the drain riser. And that is how we tested traps and vents at the Chicago Cabrini Street Testing Laboratory. We did not just depend on gravity to create enough suction. And there are tens of thousands washer drains installed just like that and NONE fo them have "siphon problems", nor could they have them.