The fact that theremins use heterodyne mixers has nothing to do with RF. The 'antennae' are not antennae in the classical, RF sense. The capacitance explanation is correct.
Capacitors and Theremin 'Antennae'
The simplest type of capacitor is a parallel-plate capacitor. That means the capacitor consists of two metal plates separated by some material called the dielectric. The equation for the capacitance of such a capacitor is C=εA/d, where ε is the permittivity of the dielectric (ε≈8.8541878176..×10^−12 F/m for air).
When you are operating a theremin, your hand is one plate (your hand is effectively grounded), the antenna is the other, and the air between the two is the dielectric. As you move your hand, you vary the capacitance between ground and the antenna. Both hands will affect both antennae, as they act like two plates in parallel, increasing the total area.
The two antennae are at right angles because that reduces the impact your left hand will have on the right antenna and vice versa. For example, as you move your hand up and down above the volume antenna, it maintains a relatively constant distance from the pitch antenna, thus it's contribution to the overall capacitance is constant (and small).
Theory of Operation
Note/Update: Please refer to FredM's Answer for a more detailed description of the oscillator.
Both antennae capacitors are part of two different, complex active LC oscillators. The 'L' refers to inductors, which store energy in a magnetic field; the 'C' refers to capacitors, which store energy in an electric field. In an LC oscillator, energy is constantly flowing back and forth between the two, changing from electric potential to magnetic potential.
The frequency of the pitch oscillator is beyond audio frequencies, so it can't be directly used. The theremin has a third oscillator that operates at a fixed frequency. The pitch oscillator and the fixed oscillator's outputs are fed into a heterodyne mixer, resulting in an output that includes the sum and difference frequencies of the two inputs. The sum frequency is even higher than the original signal, thus it is useless and is filtered out. The resulting signal is a single frequency (plus harmonics) in the audio range.
The frequency of the volume oscillator is used to control how much the audio signal is amplified. As you move your hand, the frequency changes, so the amplifier's gain changes, and thus the output volume changes.
They put them where ever they can find an opening and try to do a good job tuning them. Form comes first at apple ;) Take a look at this, they've mounted one antenna just inside the opening for the optical drive on a recent macbook pro.
Also they have a patent for a logo antenna
I once did a tear down and comparison of a bunch of apple products antennas and they performed really well compared to others in the field. Although there was that little problem with the iphone ;) So I think form comes first and then it's up to the EE team to be creative and figure out how they can get it to work.
On other cheaper laptops I think you'll find they just hide them behind plastic inserts.
Best Answer
Andy's comment is correct- this is a microstrip patch antenna, which has a hemispherical radiation pattern.
The construction is similar to a capacitor with a ground plane on the back, a dielectric (possibly ceramic in this case), and a rectangular patch on the top. It's designed to resonate at the desired frequency (1.575 GHz in this case).
The round bit is the inner feed to the patch, which is impedance matched to the receiver input through a network (a network which in microwave-world is just a pattern on the substrate).
Here is a calculator to find the dimensions, given \$\epsilon_r\$, dielectric thickness, and desired resonant frequency, and here is some info from Rogers (laminate maker) on designing your own.