The current price of the RX0 means that it’s likely to appeal to people who don’t like the ultra-wide angle / fisheye effect of the normal action cameras. It’s a shame the lens doesn’t offer a brighter aperture, as f/4 is slower than most action cameras. The small size of the camera, considering the sensor size, is quite unique, however the price is likely to make the expense difficult to justify for most people. The large sensor means low-light video should be better than most action cameras, however the lack of image stabilisation could be a deal-breaker for some.
There will be some, particularly in the professional market, that find the ability to use an external power source, plus a 24mm equivalent lens, unique and an almost perfect solution, perhaps for in-car recording, or other places where size is crucial. However, the lack of internal 4K recording makes the competition more appealing for everyone else.
If you look at the RX0 as a premium stills camera, then you could think of it as miniature Fujifilm X100 / Fujifilm X70 alternatives, except without the external controls, and with a more electronic camera feel. Whichever way you look at it, the RX0 is a tough and unique camera that you can take anywhere, without having to worry about dropping it, or getting it wet.