So basically, Through Darkest Europe but slightly better thought out?
Sort of, but not quite. In Through Darkest Europe, the divergence is primarily philosophical, which has somewhat unpleasant implications about Islam's relationship with rationalism. In my scenario the divergence is non-specific but results in the weakening of the Byzantine Empire and its conquest by the Abbasids. Moreover, in Through Darkest Europe the setting is in the present, while in my scenario it is still 1500. Things are more technologically advanced in the Islamic world and its periphery because the main centers of technological development (China, India, and Arabia) are linked. Europe remains a backwater for 2 reasons. 1 is geographic: it is a peninsula split from continental Eurasia by a mountain range and further subdivided by mountains and inland seas. This makes it difficult for information to spread and makes trade more difficult due to the lacking transportation system. 2 is political and economic. Europe has very little to trade with the Islamic world, even less than West Africa. Furthermore, Europe's states are less willing to trade with the "heathens" for national security reasons, because of Cordoba and Rum's encroachment on Iberia, Italy, and the Balkans.
Speculating forward, by 2019/2020 it is impossible to say how far this world will have progressed. However, the power disparity between Europe and the Islamic World will probably level out by 1800. The New World is an arena for countries situated on the west coast of Eurasia to benefit from, meaning Cordoba, France, Denmark, the British states, and the HRE will benefit enormously in the coming centuries. Colonialism will not be as widespread as in OTL, with the Americas being more resistant to conquest and the other continents except Australia and Antarctica already bearing developed civilizations. Southern Europe is likely to be Islamized before 1700 (although local languages and ethnic groups are unlikely to change) and Islam will be seen as part of the Roman and Hellenic tradition in TTL. Northern Europe, however, will probably remain largely Germanic. Space travel by the 18th century is likely, due to the long history of rocketry experimentation. Medicine, especially surgery, and materials science will also be ahead of OTL. Because of improved glasswork in TTL, germ theory and the cell are likely to be discovered earlier, with genetic engineering being a possibility by the mid nineteenth century.
So, by 2019/2020, TTL will not look like Through Darkest Europe so much as it will resemble a space opera with a distinct Mughal and Arabic aesthetic, with some Mesoamerican influences.
It is nice to hear that my scenario is better thought out than published AH, though.