|Map from Wikipedia|
The success of Abrahamic religions is due to the missionary zeal of Christianity and Islam. While in some places like the Middle East and the initial wave of Spanish conquests of the New World where conversions were due to top-down pressure, in many places missionary work within local societies was the primary leading cause because colonial officials' powers in places like Africa and India rarely expanded beyond the urban hubs.
The spread of Dharmaic faiths occurred because Buddhism abandoned many of the caste and ethnic-national restrictions of Hinduism which would actually make a convert to Hinduism's life worse. Buddhism with its missionizing zeal spread throughout Asia. The only reason it is not more wide spread is because it lost ground the a rapidly growing Muslim rim around the Indian Ocean and a revival of Hinduism in India.
Two points may be brought against the map and the idea Abraham's God and Dharma control almost all the world. The new great world religion is Atheism which has spread across the globe because of Communist targeting of religions and general Western Enlightenment-thought which slowly has abandoned religion. Some places like the Czech Republic probably can be thought of as truly plurality Atheist. However, in post-Christian Western Europe many immigrants, both European and Islamic, are keeping religion alive in those places.
Another objection is to call many Christians and Muslims in Africa not true Christians or Muslims. While some of these denominations do fall off the Abrahamic path with multiple gods, it is important to remember the vast majority are just adopting their culture and faith, much like Greek, Roman, and Northern European Christians did when Christianity spread throughout Europe.