Hello,
For the Friis formula, you need know the antenna parameters (gain and wavelength, or effective aperture (energy based) ). This he don't know for the electrically small dipole case, so he first has to solve that issue.
Regarding the loop case:
As htg stated, you can calculate the EMF based on the magnetic field (for electrically small loops). But with the EMF only, you don't know the power that can be extracted.
Now we place a loop in a plane wave field, with best orientation for maximum output voltage. This loop has zero resistive losses (see it as a cryogenic case). Based on the geometry you can calculate the inductance and as the frequency is known, you can calculate the reactance.
Now we add a capacitor in series to cancel the inductive component. What will be the current when I short circuit the loop, or what resistor do I have to connect to this LC circuit to derive maxim power from it (loop has zero resistance)?
This current is not infinite as the current through the loop generates a secondary far field. The far field can be calculated based on the current and the magnetic moment (product of current and area enclosed by the electrically small loop).
The energy radiated by this field (see testing test's posting) causes a so-called radiation resistance. Even a lossless coil in free space experiences a loss (due to radiation). Both for the loop and the short dipole, radiation resistance can be calculated from simple formulas, so you don't have to do the full math yourself. When you know Rs, you can calculate the theoretically maximum available power (for zero Ohms loop resistance).
By using reciprocity theorem for antennas, it is sometimes easier to see things from the transmitting case (were gain for RX is same as gain for TX).
Both a small loop and small dipole have maximum directivity of 1.5 (free space case) . From the directivity and wavelength you can calculate the effective area for the receive case (lossless case). In case of loss (what is normally the case with small loops and dipoles), you have less gain, hence less effective area. Finding the loss can be done by calculation, Q-factor measurement, etc.
The situation becomes difficult when the field isn't plane or when conducting objects are close by. The reradiated field from the loop induces current in these objects and these currents do generate a field as well. This results in a new overall radiation pattern, hence other directivity and gain. For some simple geometry you can do the calculation by hand, but nowadays a simulator can ease the work.
A special case is when the exciter (that generates the incident field) is in the near field of the receiving loop. Then the impedance of the exciters antenna will change significantly. Compare this with 2 inductivity (or electrically) coupled LC circuits (as used in wireless electric power transfer, RFID and RF Electronic Article Surveillance).