Bit.ly makes money through its enterprise service, offering custom shortened URLs (using its technology to manage shortened URLs through a branded domain, like pep.si) and advanced analytics.
Other sites are making money simply through advertising on their main site. TinyURL gets ~3,000,000 monthly unique visitors, which translates into an even higher number of page views -- the banner ads displayed on the site likely provide a good amount of revenue. URLtea.me looks like it has paid links on the front page -- because so many people are linking to the URLtea.me domain, those links likely pass a high SEO value.
Blue.gg seems to be a promotional effort / "cool factor" property for a digital creative agency. I imagine a substantial number of less popular URL shorteners are run by people simply for the cool factor or convenience of personalized, super-short links. Because these services are only redirecting people rather than serving up content of their own, the bandwidth used is really very low -- many services aren't being created to make money, because they don't cost that much money to run.