Some empires where the ruler may have claimed to subscribe to Islam were spread by the sword, but Islam itself certainly does not support conversion by the sword, instead it supports proselytising through speech and actions.

Even when the muslim ruler did conquer some place, there weren't usually any forced conversions. Much of the populations just slowly accepted and incorporated the religion into their own cultures. This is why you still have the copts in Egypt, the Zoroastrians, Parsis and Iranis in South Asia, and Hindus in India. In fact, in the early days of Islam, after Muhammad's death, the Muslim rulers prohibited conversion among the populations they conquered.

Then there are many places, such as Southeast Asia (with Indonesia, having the largest Muslim population in the world) and Central/East Africa that were never attacked or invaded by any muslim army, yet they have a muslim majority anyhow.

There are of course some exceptions to this- some Muslims kings in India apparently tried forced conversions (I'm not sure, but I think it was Mughals against Sikhs?), and there were the Almohads, as examples, but I'd say in general, over the entire course of Islamic history, that was more of an exception than the rule.