Einstein did not show that. The principal you are referring to is, ironically, Galilean relativity, and attributable to Galileo. Einstein's contribution was combining the principle of relativity with a constant speed of light.

Additionally, under both systems, relativity only applies to intertial reference frames. Rotating reference frames are detectable.

You can detect Earth's rotation without any external observations using a pendulum. Although such an experiment would not be done until Léon Foucault about 2 centuries after Galileo.

You can tell the difference between rotating and not, because a rotating reference frame is not inertial. In fact, the geocentrists knew this, because one of the longest-standing objections to the idea that the earth rotated was that you would expect a falling object to be displaced from the apparent vertical due to the rotation, these experiments were done, and the displacement was not observed (it turns out, because the effect was so small, but no-one would have the mathematical tools to work this out until Newton).