A “win” in a case against the Federal government, may, but not necessarily, would affect the private sector. Remember that the private sector is only restricted by statutes enacted under the commerce clause – whereas the Federal government is also restricted by Constitutional provisions (such as the First Amendment and the Test Act clause) which do not affect the private sector.
If they decide the case under the Civil Rights Act (enacted under the Commerce clause), holding it applies to the Federal government, the precedent would bind private companies. However if they decide the case based on Constitutional restrictions impose on the Federal government, the precedent only affects Federal (or at least, government) employers.
To clarify, if a private company decided it will discriminate on the basis of political ideology(which is not covered by the Civil Rights Act), they can do so – though the Federal government doing so would violate the First Amendment.