You are 100% correct. That is an additional resonance structure. It is equivalent to the other "most important" resonance contributor. So there are really two equally important resonance contributors.
I think this other resonance structure is "less interesting" in some ways because it doesn't show a separate atom carrying the negative charge. But that doesn't negate from the fact that it's a resonance contributor. In a very rough sense, that resonance structure helps show the aromaticity of the benzene ring.