The interferometer was floated on a pool of mercury so that it could be rotated smoothly.
Changing the travel times causes the reunited beams to go in and out of step with each other, generating changes from light to dark in the resulting image.
There really is a length contraction of the sort that Lorentz suggested, but it is not the comprehensive answer to the problem.
If you chase light in a spaceship that is moving near speed c, you will still see the light moving away from you at speed c.
Please note that this statement can never be proven. However, it is not wrong whereas the common-sense addition of velocities has been proven wrong.