Hawking is wrong about which class of jobs are threatened, and wrong about the consequences. Lower class jobs are set to be wiped out AND the results of that will be far worse than Hawking estimates, but he is right to be concerned about overpopulation and so forth.
Take an average youth looking for their starter job. Today, they might flip burgers or work a cash register or some other similar entry level job. But in the near future, a lot of fast food jobs are going to be automated. And self-checkout continues to spread.
What will the average youth do for work? There won't be a lot of options. And kids who have no jobs and no hope of getting one often fall into crime and other habits that impact society. We could easily have mobs of kids roaming cities because they have nothing else to do, and if they end up irate or angry, it could result in riots, looting, fires, etc.
It gets worse.
As we automate cars and trucks, we won't need a whole slew of other jobs. Automated cars won't crash as much so we won't need body shops and mechanics, insurance agents and related workers (this goes right into white collar workers too). Police won't write as many tickets which will directly impact many towns that depend on that revenue. Likewise lawyers and courts will suffer reduced case load from car accidents and personal injuries that don't happen, so clinics and doctors geared toward that kind of care will have fewer patients paying them.
Meanwhile, automated cars will make it far less likely for people to make impulse stops such as for fast food or snacks at gas stations. And automated cars might go refuel themselves in the middle of night to take advantage of down time or empty roads. Or they might be plug-in. In all these cases, there will be far less need for people to work at places where drivers make those stops. You won't need gas station clerks. And yes automated refueling is possible. There have been prototype robot gas stations in the works for 20 years. Only the fact that labor was cheap has kept it from becoming an option.
The net result of all these changes are a LOT of lower class people who will have no job options. And nobody is slowing down having babies. Populations are soaring. There won't be jobs for all.
Does society owe anyone a job? Probably not. But we have to realize society will demand something be done about mass unemployment and youths running rampant in the cities and towns. We'll want it fixed. Jobs are one way to try to do that. Of course there needs to be some kind of job to do. I don't see anything on the horizon that promises to employ the number of people we have now much less in 20 years.
Hawking is absolutely right that this is the biggest threat humanity has faced. It is itself a huge, dangerous issue. And one way societies have solved over population and unemployment problems is by having wars. Which is not going to be fun for anyone.