The author claims that the transition state leading to the formation of the 1,2 product from the allylic carbocation is lower in energy since the carbon (which is attached to Br in the 1,2 product) is more electrophilic.
This makes sense to me, however, doesn't the transition state represent the energies of both, the reactants, and the products? In which case the thermodynamically favored product (1,4 product) should also have a lower energy transition state.
A transition state does not ‘represent the energies of […] reactants and […] products’. A transition state is a certain arrangement of atoms somewhere between the most stable atom arrangement the reactants can have and the most stable atom arrangement the products can have. The key characteristic of a transition state is that it is directly en route from reactant to product and that it is the arrangement with the highest internal energy.
For any arrangement of atoms you can calculate a single point energy: reactants, products and the transition state. The energy difference between reactants and the transition state is colloquially known as activiation energy although that may not always be correct. It is, however, important to realise that each arrangement has its own energy that cannot a priori be deduced from any other arrangement. Thus, a transition state’s energy is not directly related to the energies of reactants or products (with the exception that by definition it must be higher in energy than both).
While it is a general rule that the transition state leading to the thermodynamically more stable products has a lower energy than any other transition state, this is not true for all cases. Indeed, for any reaction in which one can discuss kinetic (lower energy transition state) versus thermodynamic (lower energy products) control, the transition state energies must be ‘reversed’ with respect to the product energies.
