Suing Google for libel because Google misrepresents them as a dead company through purposely hiding them from customers who search for them on Google?

People who search for RapGenius on Google will find plenty of information that indicates that they are a live company, so that would be ludicrous on its face.

With Google sitting on billions in cash, I don't see how any frivolous lawsuit that RapGenius could afford to pursue without committing suicide would force them to move.

It's a reasonable conclusion for searchers to make that RapGenius doesn't exist anymore because they doesn't exist on Google

They do exist on Google. If you search for them, there is plenty of information about them.

Sure, you won't get a direct link to their site, but there is plenty of evidence that they exist that Google provides, including explanations of why the direct link doesn't appear. (E.g., for me right now, the first result if I search for "Rap Genius" is a news result with a time of "3 hours ago" titled "Google punishes Rap Genius for manipulative SEO tactics".

I don't think that anyone would reasonably conclude from that the RapGenius doesn't exist any more.