(Ignoring all other posts to answer the OP)
I'm currently taking History of European Civilization III at the Golden Gate Academy (San Francisco) and this question recently got me thinking as a matter of fact. So much so that I began discussing the topic with my professor.
Frankly, we're surprised that the IR did not happen in Europe; despite its appearance today. For one, Europe had all the easily accessible resources required for the revolution in places such as England, Lorraine, and Silesia. Two, though Christian Europe is only comprised of Iberia, France, Germany (Hamburg to Rome), Naples, the Commonwealth (Poland and Sweden to the Urals), and Denmark-Norway -- point being not so many different countries -- there are many, many ethnic groups scattered across the continent. Had the Hapsburg Dynasty not won the 60 years war in the 17th century, perhaps (1) the Holy Roman Empire would have fragmented and (2) the pacification of Europe would not have been successful. This would have led to more conflict, greater cultural diffusion and thus more progress. Furthermore the Catholic Church would not have been powerful enough to instill such restrictive laws on the Christian populace of Europe.
Three, the failure of the last crusade to liberate Magyaristan, or Hungary as it was once called was both a missed opportunity for a turning point in Perso-Arab hegemony/Christian retrogression.
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Though you bring up a new topic to consider supplementary to why Europe wasn't the first to experience the IR: what would the world look like had Europe experienced the IR.
Let's go back to my earlier scenario where the Hapsburgs lost the 60 Years War. For the sake of reasoning, have the war end in the 50s instead of the 70s due to a divergence in the 20s/ early 30s where the Commonwealth goes under a secular revolution due to the newly acquired protestant territories of Sweden and the Orthodox territory of Russia. Have the result be France getting involved sooner rather than later and butterfly the Commonwealth dog-piling on. This would surely lead to the collapse of Austria and Spain as well as the entire Catholic Church for that matter (we need to give Europe as many ways as possible to push forward in order to contemplate how the world would look with an industrial Europe; even if they may seem far fetched).
Fast forward about a hundred years. The Holy Roman Empire is Hindered (TTL Balkanized... India fragmented), Spain is reduced to Galicia, Castille, and Aragon, Italy remains fragmented, the Commonwealth (with its new territories and learned tactics) has made strides passed the Urals, and Europe is under a new reformed leadership in the west and secular leadership in the east.
Lets have the IR start in (now) Polish Silesia through the use of simple steam power as what happened in Persian Mazandaran and quickly spread its way west to Lorraine and modern day Northwest Germany and east to the riches of western Siberia. That will snowball Christian Europe of the early 19th century into a society as advanced as OTL's Orient (TTL's term for the Middle East, while East Asia is known as [toponym of whatever the Arabs called the Pacific before Magellan's time] TTL -- did a a lot of research on the subject and found nothing). This doesn't mean that they would be ahead of the Arabs nor Persians, but at least on par.
So now that we have the back-story established, we can speculate on what the world would look like by the 1900s. The real question is one of imperialism. Would they colonize and conquer like the Muslims or simply build up their economy like the Asians? I definitely believe the former. Unlike Asia, Europe cannot sustain populations of enormous magnitudes and thus would have to look abroad for markets for the industrial goods they produce.
Therefore, we are looking at an Age of Imperialism contested between the Muslims and Christians. East Africa will fall Muslim as OTL; however West Africa will probably go Christian (Mali is a toss up, as it may go independent like OTL). With this new competition, there may not be a sovereign native country in the northern New World (imagine New Jersey as the south, Michigan as the southwest, and Alberta as the northwest). In fact, the east coast of the entire New World could potentially be dominated by imperial Christians as opposed to the converted Mesoamericans and the Arabs due to geography. The south [Pacific] would definitely not be European, but I can imagine, even with butterflies, that the northwest New World would still be colonized by the [toponym for the Arab word for Pacific] powers.
So that's what the world would look like I'd imagine by the 1900s. Afterwards, who knows? Wow. This got me amped. I can't wait to discuss this with my professor. I'll let you all know what he has to say.
(Notes: PoD from OTL 1400s, no age of discovery. However, history plays out the same across the globe minus the Colombian exchange, etc. Even the 30 Years War plays out similarly around the same time despite being 200 years after my PoD.)
(Well, I typed way more than I expected to and learned a lot in doing so. I hope this post was appreciated. I had a grand time writing it.)