Granada was the last bastion of the moors in Spain. They were kicked out by the catholic kings (king and queen) in the same year as Columbus "discovered" america, 1492.
The albaicin is an area along the smaller river in Granada which runs past la alhambra. It is now the gypsy area and you are likely to be robbed if you go there at night. There is nothing islamic about it, unless it has changed drastically in the last 7 years since I lived there.
I would suggest that perhaps the author is writing about "today" as a period in time in the past, after the moors were kicked out, or even before hand. But that is not the Granada of today!