Interesting article, kid.
I noted the numbers were about 8,500 a year on the average according to the study, so if raids/kidnappings were as spread out as the study indicates, and included ships whose loss might be due to storms or rotten hulls, then the bleeding was probably not enough for the various European rulers (who were quite busy bashing each other) to want to take on the Ottomans, who were still a considerable power in the Med at this time.
Virtually every society upon this earth has enslaved other people at one time or another in their history...some areas (Sudan is most often accused) may practice it yet.
This civilization thing, it can be a thin veneer at times.