Since this case upheld a law prohibiting same-sex couples from engaging in sexual activity, it is a stretch to say that it indicated that the rights revolution was "here to stay." However, if that is the argument you must make, you should argue that it is because the Court did not overturn the entire idea of the right to privacy.
The right to privacy, as found by the Court in cases like Griswold and Roe, was a major part of the rights revolution. It is conceivable that the Court in Bowers could have upheld the conviction by overturning the whole doctrine of the right to privacy. Instead, the Court chose to find that there was a right to privacy but that that right did not extend to homosexual conduct.
Thus, you can argue that this case was a win for the rights revolution because it did not overturn the doctrine of the right to privacy.