NFC / Near Field Communication is a very special subset of electromagnetic communications (not just a marketing term - although many purveyors probably have no idea of the underlying differences between NFC and "proper" RF).
Note that NFC (Near Field Communications) is essentially technically identical to another "buzz word" technology IPT - Inductive Power Transfer. The difference is more applications emphasis that technology - both are mentioned below and information on one will be useful to understanding aspects of the other.
As you note, at close proximity to the antenna (how close varies somewhat with antenna design and other parameters) the relationship between magnetic and electric field components has not "settled" down to that which is experienced in "free space". (Note that this is another way of looking at the same relationship as explained (superbly) in the reference below which talks in terms of the "flatness" of the radiation pattern.
In free space the fixed relationship gives rise to the characteristic impedance of ~= 377 ohms.
Wikipedia on impedance of free space - warning: Maxwell lurks here :-).
Here is a superb explanation of WHY far field impedance settles down to a (nearly) constant value and where it breaks down (under about 1/6th wavelength) and the implications. They say (somewhat edited by me) -
As noted in the sections on RF propagation and the radar equation, electromagnetic radiation expands
When the range is large, the spherical surface of uniform power density appears flat to a receiving antenna
which is very small compared to the surface of the sphere. This is why the far field wave front is considered planar and
the rays approximately parallel. Also, it is apparent that at some shorter range, the spherical surface no longer appears
flat, even to a very small receiving antenna.
The distances where the planer, parallel ray approximation breaks down is known as the near field. The
crossover distance between near and far fields (R ) is taken to be where the phase error is 1/16 of a wavelength, or about 22.5 degrees
Radius_near/far crossover = 2 x D^2 / wavelength
where D is the largest dimension of the transmit antenna.
For interest, the near field of the Jodrell Bank Radio Telescope extends into near-earth space, making it "hard" to test it with intra solar system spacecraft communications systems which the dish is designed to interact with, prior to launch.
The (probably) most significant implication of working well within the near field was mentioned in passing by Steven. In the NF coupling is largely magnetic. No energy is dissipated in a magnetic field unless the field is "loaded". A NF "transmitter" can operate at low power level until a tuned circuit couples to the field. At this point "transmitter" power level will need to be increased to maintain drive voltage level (or will automatically increase in a system with low impedance drive to the transmit "tank" circuit. The corollary of this is that the presence of a receiver can be detected by the effect on the transmitter. Receiving IS transmitting effectively.
Also, for explicit power transfer operations such as laptop of other battery charging the transmit power level can be low when unloaded, be increased by loading - such as when a laptop etc is presented for charging, and decrease when the target is charged and elects to stop accepting current. This is the area dealt with by "Inductive power Transfer" (IPT)
These characteristics of near field coupling which may seem "a bit magic" when seen from an RF perspective, seem entirely normal when seen from a transformer coupling perspective.
A difference to normal transformer coupling practice (and much closer to what is seen with RF) is that power transfer can be very much improved by resonating the receiver coil.
Higher "Q" allows greater range. Power transmissions at distances of metres are possible at high Q. I don't have details of Tesla's Crystal Palace equipment but reports sound like he may have managed even further. Warning - much material on Tesla on web is bunkum.
Diagram below - Tesla "magnifier" -
Involvement of free space impedance on typical antenna impedances are discussed in
Near Field power transfer system - they don't use the term anywhere in the associated page
Philips PN532 NFC communications system.
NXP Near Field Communication
(NFC) for handheld devices and
POS terminals PN53 - Datasheet