Board requirements for a chip PCB antenna?
To me, this picture from page 9 of the datasheet answers it all:



This shows a ground plane on the outer (upper) layer. The chip antenna is soldered directly on top of this layer. Part of the ground plane is covered with solder mask (see the other picture on page 9, only 4 holes are left for the chip antenna to solder on to). The area marked 1 is where the signal connection is.
2, 3 and 4 are grounded.

The ground plane shields the antenna from "seeing" what's underneath so what is there doesn't matter so much. For best performance you would leave the other side (behind the ground plane) of the PCB free of any components but if you must you can put electronics there as well.

Since for the antenna you need only 1 layer, indeed you could make this on a single layer PCB. I would extend the ground plane down as far as you can allow it to, but more than 2 cm might be overkill and not needed.

The active antenna (Antenova Sinica) has a different antenna design, part of the antenna goes under the module so it cannot sit directly on a ground plane as that ground plane would be too close to the antenna. That's why the keep-out area is needed, the Antenova Sinica's antenna also needs to "see" through the module and through the PCB it is mounted on. It's a different design and so has different requirements.