Probably checking the computer installed for diagnostics of the autopilot system. If it's in self driving mode and you are the engineer in charge, you'd want to constantly check what the system is seeing vs the actual conditions on the road.
To me it looks like the guy is just falling asleep at a boring job. In all likelihood that was not an engineer more than any other taxi driver is an engineer.
The software is the "driver" of this car. Not the human behind the wheel. Take a look at job descriptions [0] for this. They always include a bit about "operating in vehicle computers". The fact, we don't know what the person is doing.
0 - https://www.indeed.com/viewjob?jk=597616bf7d02d899&tk=1c96sl...
I don't know about current regulations. Are companies now allowed to operate autonomous cars without a driver that pays attention?