Maybe Spock couldn't date the structures themselves, but rather was able to date events that collapsed the structures.Spock actually said the ruins were "On the order of ten thousand centuries old."
That's a million years; of course, still nowhere near the age of our solar system. Radiometric dating in the 1920s and 1930s indicated that the solar system was at least a couple billion years old. And the numbers got more accurate in the next few decades after that.
Spock could have been making a very conservative estimate. It wouldn't be the only time he wasn't quite correct about something.
Kor