There are two levels on which to answer this question, the literal and the figurative.
Literally, when Gardiner refers to the "rule of the road," he is talking about the rules that govern what you are allowed to do on the road. He is referring to the anecdote about the Russian woman walking down the middle of the road and causing traffic problems. That woman was not following the laws that govern what we may do on roads.
But there is a figurative meaning here as well. Gardiner is using traffic laws as a metaphor for the rules (often unwritten and informal) that make society work and that create community and solidarity in society. The major point of this essay is that people need to think about how their actions affect others and how they affect society, not just about what they themselves want to do. In this sense, the rules of the road are rules of politeness and of unselfishness. They are rules such as "don't play your trombone too loudly or at the wrong time" or "don't have loud conversations in public places."
So, the term "rules of the road" is being used in two ways in this essay.