The social dynamics are themselves a dimension. Social network graphs can behave as fractals. In a gymnasium filled with people, there is a significant 'fractallyness' to the social network. In traffic, the fractallyness is very limited to just about all the people in the road near you. The social graph, though more fluid in a traffic jam than a pep-rally, is still fairly small.
3Blue1Brown has a great video on the dimensionality of fractals [0] that is useful here. I'm just going to spitball, but I'd bet that the dimensionality of the social graph of a traffic jam is really close to 1.
So in the end, the DoFs of a traffic jam are probably very close to 3, but just a bit over. Say, 3.14-ish. ;)
