Nothing necessitates Islam specifically. However, it is untrue to say that the Byzantines as opposed to the Romans and Greeks innovated in the areas that Islamic civilizations did. The Byzantine state was not hostile to innovation, and indeed showed a remarkable capacity to reform itself following severe challenges. However, the article mentions little if anything on innovations in areas such as astronomy and mechanics, which alongside other things leads me to conclude in certain areas, the Byzantine Empire was just as conductive to the development of science as the Caliphate was. If you have anything to disprove this I'd be interested in seeing this.
I'm not quite sure what your second point is trying to say. Most scientific theory is based on what has gone before, and it is likely that any development in the Early Middle Ages would be based on the works of the classics. As for the point about the Persian scientists, my point isn't about Muslims having some natural scientific ability lacked by others, but that the Caliphate produced an environment more conductive to scientific research than either Sassanid Persia or Byzantium.
I remember reading someone making a point on the board a year ago that the Arab desertification of North Africa was a myth propagated by the French in the 19th century to justify their colonialism. It was based largely on selective readings of ancient sources to exaggerate the previous productivity of North Africa as a granary. Unfortunately I can't find any sources to back this up at the moment.
Actually, Albert Hourani notes that the first few centuries of Islamic rule "led to the growth of large cities", largely due to the absorption of such a large area into a single Empire, which created an enormous economic unit and so forth. If one is to go off the "Big History" perspective and believe that innovation is the result of increasingly complex societies which are made up of larger numbers of potential innovators, there is a compelling case that the creation of the Caliphate, and the subsequent unit of the "Muslim World" was indeed an advantage for scientific innovation that Byzantium and the Sassanid Empire lacked.
But did the Khilafah really benefit from its new found empire? Or did it squander it after a short period of disastrous revolt? The fact is that the Khilafah whether Umayyad or Abbasid were crushed (as far as actual real power) after only a short time of power. This as I have asserted earlier was due to the incredible instability of the Khilafah due to:
1. The decadence of the Abbasid royal family and their little clique of sorts in Baghdad who were primarirly pro Arab and extreme noble Mu'tazalites. It is hard to be the Khilafah the righteous defender of the faith and sword of Islam and commander of the faithful whenever you have a court full of scholars who commit Bidaa and say that what is obviously haram (to the general population) is really Halal and the allowing of Qarmations to tear up Makkah and desecrate the ZamZam well. As well, in many cases the Khilafah didn't even rule and was dominated by his court as in the case of Al-Radi bi-llah and Muhammad ibn Ra'iq.
2. The use of runaway rural slavery and the castration of its African slaves. For some reason Arab slave traders during the Umayyad and Abbasid period feared myths on African fertility and to remedy their fears Zanj slaves were universally castrated. This caused a problem, if you need constant slaves for you rural agriculture or just because Arabs of the day used slaves as everyday gifts and bargaining tools (it was a currency if you like) and the slaves aren't reproducing then that means wars must constantly be fought to regain the supply, which kept the Khilafah at almost a constant state of war. As well, the toil of these slaves was evident and was used by the Shurha to incite massive revolts, revolts and instability that would bring the fragile Khilafah to its knees.
3. The use and reliance upon Turkish Mamluk slaves. Again this is a negative effect of decadence and weakness of the Arab noble class. This did much to break the notion of the need for a Khilafah and questioned legitimacy especially when a Khilafah is killed by his Turkish slave and Allah doesn't rebuke the slave. Things like this go a long way and destroying the legitimacy of the commander of the faithful and his Arab noble class.
4. The religious instability of a decadent state. Again a decadent state who claims such high religious power cannot seem weak and decadent to his people, but the Abbasids did and instead of growth we saw instability in the form of sectarianism with Shia coming out of Taqqiyyah in Arabia and Iraq to put one of the Ahl Al-Bayt on the throne opposed to the decadent and weak Khilafah, this was finally realized with the rise of the Fatimids and built upon by the Qarmations or the Bahrain revolts.
5. The lack of real Islamic backing and no real authority according to Fiqh. This can be seen in how the Khilafah disregarded the Shura councils and preferred dynastic succession, what happens when the population catches on and realizes hey, these guys aren't doing it as is prescribed in the Quran or in the Sunnah. This gave the Shurha wood to toss into the flame for its war against the Arab hierarchy and led to its large following, but afterwards Islamic states did not claim the title so heavily and because it did not claim the title it did not have to act so on the dotted line as the Abbasids had to. Also it helps whenever you no longer use slaves for every type of transaction lol.
Now tell me how a state (Sassanids, Byzantium and Ethiopia) who lacked these problems (had there own but still) would not have innovated itself, especially after the Hellenic world recovers from the plague of Justinian and Byzantium possibly recreates Pax Romana.