"Rappers Who Spin Vocab Like Shakespeare"
I think the technical answer to the question is that the word "spin" is being used in place of the word "use".
Example: I like rappers who use vocabulary as deftly and poetically as Shakespeare did.
The phrase basically means:
"Rappers who are just as talented with their words as Shakespeare was with his."
In essence, that kind of spin means 'to put a spin on', or 'to be creative with'.
If I said, 'I made Chinese food with an American spin', I would mean that I got creative with my cooking, and changed an original Chinese recipe, making it more American.