This is all about car systems but should be similar to the bike rotors.
The car rotors I deal with are Carbon-Fibre re-enforced but with short, chopped strand fibres.
The bike rotors in that article appear to show a woven Carbon Fibre material which will make them a bit tougher.
But they are hard and inflexible and they will chip like any Ceramic material. Silicon Carbide is about third in hardness tables, not far behind Diamond. It's very rare in nature and tends to be found in meteorite craters
Small chips in the rotor are tolerable but there are strict limits. Anything over a certain size will write-off the rotor.
Wear - is a tricky issue. On a car you have to remove the disc and weigh it to figure out if it's worn out as they don't get thinner like Iron discs do. However they do last about 3-5 times as long as an equivalent rotor on a car.
CTE - Co-efficient of Thermal Expansion is much lower than Iron. About a third, so less distortion with heat. Therefore less risk of dragging or rubbing on the pads 'off-brake' if you get them hot.
Last thing - car systems use special pad materials with these rotors.