The load has some voltage drop in it, hence electric field. Together with magnetic field, this brings the energy in. Same way, the source generates voltage and, together with magnetic field, this brings the energy out.
Direction of electromagnetic energy flow is determined by the Poynting vector, E × H, and depends on both voltage polarity (through E) and current direction (through H).
As I understand it, even in DC circuit energy flows from source to load thru the space in direction of Poynting Vector.