Frankly? It doesn't. Sure it is painted in a style typical to the renaissance period. But that does not make the man who painted it a renaissance man.
http://en.wikipedia.org/wiki/Polymath
A renaissance man is another term for a polymath. Or more commonly "Jack of all trades" and master in all as well. So just this painting makes him a renaissance painter. All the other stuff he did like anatomist, architect, inventor on top of that makes him a renaissance man.