Welcome to the forum.
As stated above, it isn't possible to zone-focus on the RX100. It is, however, possible to "dummy" zone-focus by the following method.
1. Make a note of the following data for calculating Hyperfocal Distance (HFD):-
Focal length (effective) ..................... HFD (in metres)
28mm ................................................. 10/Av
35mm ................................................. 15/Av
40mm ................................................. 20/Av
50mm ................................................. 31/Av
70mm ................................................. 61/Av
85mm ................................................. 89/Av
100mm ............................................... 123/Av
2. Set the centre button to toggle between AF and MF (see user manual - page 130)
3. Set desired focal length
4. Set desired aperture (in Av mode)
5. Point the camera at an object which is at the calculated HFD and focus (using AF)
6. Toggle to MF and the focus distance is then locked until you either adjust it, or toggle back to AF.
Note that the HFD calculations above have been rounded to provide integers for ease of use. Self-evidently, this method is a lot less convenient than using HFD on a manual lens, and also requires a good ability to estimate distance.
It does take a couple of attempts to get comfortable with this method, but it does work. Hope it helps... good luck.