I don't see insurance dying overnight, but if their cars are
solely used in driverless mode[1] then it's in the manufacturers' interest to take on that risk directly: since they're ultimately liable for [virtually] all risks cars are compulsorily insured for[2] it makes sense to cut out the middle men and keep that float to themselves as well as streamlining the claims process. The ability to make mandatory insurance contingent on getting cars serviced expensively at approved dealers is a nice little bonus. So you get the mandatory insurance certificate with the car,[3] and a whole bunch of B2C auto brokers and insurers are left selling policies which are entirely optional and which consumers consider much more unlikely to be claimed on
Sure, some parts of the industry (Lloyds reinsurance syndicates underwriting the portion of the manufacturers' liability they're not willing to self-insure, which is probably the idiosyncratic risk of a negligence claim over software updates) still exist, but all those B2C players are fighting for a much smaller share of the pie which continues to decline as more people switch to exclusively driverless cars and they don't really get stolen any more.
[1]I think this is a very big if in the foreseeable future, but it seems to be assumed by the article.
[2]there's still a market for insurance against vandalism, fires not caused by the car itself and [to a much more limited than before extent] theft, but that's probably not compulsory in most jurisdictions and so a much tougher sell for the insurance companies.
[3] they could even build in the annual policy renewal fee for the design life of the vehicle into the purchase price if they really wanted to. I'm also assuming here that there's no legal impediment to individuals' motor liabilities being underwritten by a division of the vehicle's manufacturers in most jurisdictions.