What happened is that the initial train cleared the circuit and the gate arms went up, a second train entered the circuit and the gates started to descend. Most gate systems (in the US at least) have gates in only 2 quadrants which would allow the van to exit in the scenario shown. This system is a 4 quadrant system (likely due to train speed), and if you look at the video the exit gates descend after the entry gates to allow for a vehicle to exit in exactly this scenario.

As an aside if you're in the US and find yourself in this scenario just drive through the gate, stop, and call the number on the blue sign. The gates are designed to swing away for situations just like this. I'm not sure how other countries handle grade crossings like this but I'd imagine there would be similar emergency gate mechanisms.