Should unemployment caused by the government closing non-essential businesses during quarantine be counted as structrural unemployment? I have following definition of structural unemployment (taken from "Modern principles of economics" by Tyler Cowen and Alex Tabarrok):


  Long-term unemployment caused by shocks or permanent features of economy making it harder for certain workers to find a job


So the answer to the question in the title would seem to be "No, because quarantine won't last so long that prices of wages and other factors of production would fully adjust to inflation. So unemployment wouldn't be long-term, thus it wouldn't be structrual unemployment". 

But on the other hand, other three types of unemployment (seasonal, frictional, cyclical) don't seem to fit the bill. An example: Suppose prostituion is legal and I'm a prostitute. Due to pandemic the government decides that prostitution isn't an essential business and because it's not something that can be done online brothels are forced to be closed, including my brothel. My brothel is also a small business with very thin profit margins (consequence of very competitive market caused by low price of entering the market). In short, without its workers working it's unable to pay its rent and is kicked out by its landlord, spelling end to it. I try to find another job, but due to many other businesses closing down competition for very few vacant jobs is crazy and they disappear with speed of light. Is my unemployment seasonal? No, we don't have seasonal nationwide quarantines. Is it cyclical? No, because even if economy was booming nationwide quarantine and ban on non-essential businesses would still leave me and many other people without job. Is it frictional? No, I'm fairly certain that there is no a vacant job that is waiting for me to find it. Structrual unemployment seems to be closest to that I experience by its sprit. So, maybe the definition is too narrow and it's possible for unemployment be both short-run and structrual?
There are lots of different people unemployed, and the answer will be different depending on the person. In your prostitute example, if you left your medical assistant job because prostitution paid more, then it's frictional, because there are lots of medical assistant jobs, but it might take you time to go through the interview process and be onboarded. If you have no marketable skills other than sex work, then it's structural unemployment. If there is another job that you're qualified, but you don't get the job because there are so many other people competing for it, then it's cyclical (which is a bit of a misleading term, since there it's not like there's a "quarantine/no quarantine" cycle, at least not yet, fingers crossed).