No, this vehicle as well as similar "hybrid" vehicles are designed to work this way. The gasoline-fueled part of the system will keep the batteries properly charged.
This vehicle only has a very limited electric-only range (30-40 miles is what the ads say) and so unless your trips are always under this limit, the vehicle is going to be running on gasoline ...
I can relate a story from my own experience with my daughter's car. Turns out it had two bad ignition coils that caused the engine to misfire when it was raining. Did she stop when the check engine light came on? Nope!
So the unburned fuel from the misfiring cylinders ends up in the catalytic converter. These things are designed to handle mostly burned ...
I'd bet a lot of money that that light indicates that the anti-theft system in the car is activated - meaning that the alarm will go off if someone tries to break in.
This would explain why it's only activated when you're out of the car and the doors are locked. The light looks exactly the same as on my Jeep.
This is what the Prius plug-in manual says:
Notice about fuel
●For plug-in hybrid vehicles, fuel may remain in the tank for a long time and
undergo changes in quality depending on the how the vehicle is used.
Refuel at least 5.3 gal.(20 L, 4.4 Imp.gal.) of fuel every 12 months (refuel a
total of at least 5.3 gal. [20 L, 4.4 Imp.gal.] over a 12-...