He explains all the terms at the start of the book. He has his own definition for capital which also includes real-estate etc... OP's post is just an argument

He explains all the terms at the start of the book. He has his own definition for capital which also includes real-estate etc... OP's post is just an argument against a straw man. BTW. Piketty also says that the problem with modern economics is too much focus on fancy math.