contextual meaning of "dynamics"
From Merriam-Webster, this is the closest definition:
dictionary.com has a definition similar to the one you quoted, but also one that may be closer to the way it's being used in your quote:
2 (used with a plural verb) the motivating or driving forces, physical or moral, in any field.
It's referring to the complex relationships between all the economic and social processes and forces related to the sharing economy.