It might seem a bit alien to us for them to be able to sleep with their eyes open...but just because they don't have the same physiology as we do with regard to eyelids doesn't mean they can't/don't sleep.
Picture this...an alien race comes down to visit the earth and get to know mankind. These aliens have big triangular ears that are very sensitive to sounds. When they sleep, they not only close their eyes, but they fold their ears over and close them up tight as well...to shut out all but the most urgent sounds around them. And they can't understand how human beings can possibly sleep with their ears wide open, able to take in every little sound going on around them.![]()