There are many, many different designs for antennas, and some designs are quite unusual. Antennas commonly use a ground plane, but this is not a strict requirement. A loop antenna and a dipole are two examples that don't require a ground plane.
The basic requirements for an antenna are:
a good match to the circuit driving it (and almost always resonant
at the operating frequency), so that the most power possible can be
put into the antenna, and
having current flowing along its length, so that the resulting
fields radiate that energy into space. (Receiving antennas are just
this process in reverse).
Item (2) explains why you can't just stick a small tank circuit on a board and expect it to radiate efficiently.
Item (1) generally comes under the topic of "tuning", where you bring the antenna into resonance or wherever it was designed to be tuned. A dipole antenna is effectively a resonant length of wire broken in the middle to allow the feedpoint to be inserted. A "ground plane" antenna removes half the dipole and substitutes the ground plane for that. The inductance of the radiating element works with the capacitance between it and the ground plane to form the resonant circuit that gives the antenna proper tuning. When used this way, the ground plane may be called a "counterpoise".
A helical antenna coils up the radiator somewhat, to increase the inductance and shorten the length. Shortening the antenna affects its performance, as mentioned earlier.
So far, we've got a coiled radiator sticking up above a ground plane. But they've got a surface-mount version that lies parallel to the board. I can't tell from the data sheet if both ends are connected, but I have to guess that one end is still open...it's just soldered down in order to hold it in place. If you bring this arrangement too close to the ground plane, it will add capacitance to the circuit and detune it a lower frequency. Some of the energy will also be coupled to the ground and be lost, or at least upset the intended radiation pattern.
The designer has tried to indicate on the schematic the way the grounds should be separated, and done a reasonable job with the standard symbols available to him.
There ought to be a detailed description and written guidelines in the datasheet, and recommended PCB layouts either there, or in a separate Application Note (if you look up this chip on the TI website, the relevant App Notes should be easy to find)
But basically, the IC contains both a high gain amplifier with a sensitive input, and a high current switch, capable of generating a lot of noise. With incorrect grounding, high currents in the ground wires can generate unwanted signals on the amplifier input, causing instability or poor voltage regulation.
The solution is to - as far as practical - provide two separate grounds; one quiet one for sensitive signals (denoted by "earth ground" ) and one for high currents (denoted by chassis ground, which doesn't have to be connected to the actual chassis!) The two MUST be tied together - at one, carefully chosen point, sometimes called a "star earth" (useful search term for further reading!)
Thus R1 and R2 provide the voltage feedback to the error amplifier. You don't want to inject large errors via R2, so it is returned to the quiet ground. The error amplifier will take its reference from the "GND" pin (again on the quiet ground)
Now...
Switching current through L imposes a huge AC current waveform on Vin, and generates a huge AC current on Vout respectively. These currents are communicated to ground via C1 and C2 respectively.
In fact the power side of this circuit can be read as one continuous loop GND -> C1 -> L1 -> (switch inside chip between L and Vout) -> C2 -> GND.
This loop is the most important part of the circuit and must be kept as small as possible. Best thing to do is to put the GND leads of C1 and C2 right next to each other - virtually all the AC current goes from one C pin directly to the other. The other connections (PGND, VAUX via C3) are less important but go to this point too.
And one (reasonably thick) trace from here to the low noise ground will carry relatively little current, with relatively little noise on it.
Learning to read this high current path and keep it separate from low noise ground will go a long way to making your switchers trouble free.
Best Answer
Yes, the grounds do come back to the battery if you follow the traces or conductivity.
But that is not what they are really saying.
What they are are saying is separate the loop currents for power and control. You want to ensure that they are separated.
Notice how the PGND is kept away from everything else ? The high frequency nature of SMPS means that there can be some noisy current paths and by controlling their path, and what they are allowed to interfere with, helps control noise, and EMI.