Bigger than Google, yeah ok. $300 billion market cap, $50 billion in cash, $50 billion in sales, within 15 years.
The outcome for Rap Genius is far more likely to be that of a Hunch, than a Google. I've yet to see anything about Rap Genius that suggests their technology or approach will yield such a breathtaking commercial windfall as Google. Even their reach is pretty mediocre for a nearly three year old service (speaking in terms of the huge future outcome they pander to for headlines). See Pinterest for a comparison on size (they're 15 times larger than Rap Genius), and those guys don't go around claiming to be the next zillion dollar company. Zero chance Rap Genius can springboard that to Google like results. Google was at the center of the most important Web utility of its time: the ability to accurately and quickly find anything online; and their technology was mind boggling good. Rap Genius is more like Wikipedia - it's a content solution provided by the user base, and there isn't anything earth shattering about that (see: Answers.com or Quora).
I'd say that within 24 to 36 months they'll pivot or be sold. Reality usually hits like a hammer when you proclaim yourself the next Google (or Facebook).