Question: I am amused by the story of Beethoven dueling another composer in Vienna, in which he takes the other composer's music, puts it upside down, and proceeds to humiliate him. I feel as though keyboardists with that kind of talent must exist nowadays, but they are perhaps not as popular as they once were.

Do we have such "Rockstar" pianists in the modern age? Who are they?

Answer: 
The type of keyboard music typically composed during the classical age was so much less complex, and the number of professional musicians was so much smaller, that the comparison cannot be made in any reasonable way. 

A lot of present-day pianists could probably sight-read the music of a second-rate composer from 1800. But that was a time when the music of Liszt, Alkan, Ligeti, Messiaen etc. etc. did not exist, and would have been considered absurd and obviously unplayable. It is impossible to say whether there are living musicians who are as phenomenal by current standards as Beethoven was by *his era's* standards.
You should definitely check out keyboardists from progressive rock bands. Prog rock musicians really introduced synthesizers to the popular music/rock scene and elicited really unconventional sounds from those synthesizers. Listen to what they'd done with synthesizers in the 70s, and you'd be amazed. That was 50 years ago!

The most famous keyboard giants of prog rock are probably Keith Emerson of the band Emerson, Lake and Palmer, known for his flamboyant live performances and unconventional techniques (e.g. sticking a knife into a keyboard), and Rick Wakeman of the band Yes, who was much less flamboyant but nevertheless a great keyboardist who created many interesting sounds.

My favorite, however, is Rick Wright of the venerable Pink Floyd; he wasn't into doing crazy, virtuosic things with his keyboards, but he was really good at creating sounds and conveying moods and atmospheres with his synths.