The short answer is mostly yes.
Standard Homeowners coverage (ISO HO-02: Broad Form), Renters (ISO HO-04: Contents Broad Form) both cover "Riot or Civil Commotion" without definition. It's Peril #4. Obviously, depends on your policy (because on the off chance you have a non-ISO form, it might exclude riot) and because of endorsements/exclusions/etc. But the core policy covers it.
Commercial Property insurance also covers riots. See ISO CP 10-10-06-07 (Causes of Loss: Basic Form). Peril #7 is "Riot and Civil Commotion" and includes "acts of striking employees while occupying the described premises" and "looting at the time and place of a riot or civil commotion". So those 7-Elevens would probably be covered (again barring exclusions/endorsements/etc.) I don't have the definitions form in front of me, but I doubt they bothered to define terms because they did not in the HO forms. There's also CP coverage for vandalism, but not theft.
As for Automobiles, a recent MAIF policy (i.e. the nearest autoinsurance policy to hand) showed Comprehensive and Collision coverage and no relevant exclusions. (Although if you were using your automobile to loot Mondawmin Mall and the police get your plates and use civil forfeiture to take your car, that would be excluded.)
There is a little case law on this but there are interesting disputes. Business interruption claims based on curfews. Disputes about what counts as a riot. Disputes about losses caused by government actions during a riot. Disputes about thefts during riots that took place at the same time as fires. Disputes about how this relates to terrorism and war coverage/exclusions. Even a case about whether a runaway slave killed by a slave patrol was covered. Etc.
So basically, if everyone had insurance (big IF there), that insurance will (all things equal, no exlcusions, assuming they used ISO forms, etc.) pay.