Wow, there are so many problems with that article I don't know where to begin.
Firstly, it is taking really modern trends and extrapolating. The author hasn't shown one nation there that started as a 'Open, free, democratic society' which followed the curve they extrapolate. It's also ignoring nations which don't fit the curve, like Iran which was pretty secular and open whilst still being largely, if not totally, Muslim.
Bosnia is another major outlier. The population has been about 50% Bosniak Muslim, 30% Serb Christian and 20% Croat Catholic even while a part of Yugoslavia, in the nineties it was largely (but not exclusively) Serbs bombing and massacring Bosniak Muslims. Nowadays, it is amazing how modern and multicultural Bosnia is. In Sarajevo it's not uncommon to see women in full hijab walking alongside office women in short skirts.
There are a number of glaring problems with some of the countries in the 10% bracket, like India, where Muslims have been massacred by Hindu nationalists, and Chechnya in Russia which... do we need to go into why Chechnya is radically atypical?
The 60% bracket also includes figures which are radical reversals of the truth. they note that it includes: 'sporadic ethnic cleansing (genocide)' and includes Albania where, again, the ethnic cleansing and genocide was often targeted at Turkish Muslims under Serbian Christians.
The whole piece takes isolated examples, massive overstatements, blatant historical distortions, and flat-out lies and weaves them into a story which fails to describe even one country which has travelled the path they lay out from 0% Muslim multi-cultural society to total 100% Muslim control.