Christianity does seem to be unique in the sense that salvation isn't just revealed in history, but consists in a specific event. The sacrifice of Jesus as a substitutionary offering must have occurred in historical fact if the claims of Christianity are to be accepted. By contrast, the teachings of most other religions would be little changed if the history of their foundation were partially or even substantially altered.
To take a handy example, Gautama Buddha famously discovered the Four Noble Truths while meditating under a pipal tree. While this does make the tree sacred to Buddhists, it really wouldn't change they what believe about Enlightenment if he sat under some other tree. In many ways, the thing that makes the Buddha important is that he was an ordinary man who made an extraordinary discovery. If some other individual had discovered the Four Noble Truths, they might have been called "the enlightened one" instead. So there's no particular urgency for Buddhist apologists to demonstrate that any particular historical event actually occurred.
On the other hand, many religions do place a high importance on historical details. Many Jews would be shaken if it could be proven that the Exodus did not occur. The divide between Shia and Sunni Muslims dates back to understanding of specific events going right back to the potential successors of Muhammad. And there are plenty of Christians who deny (or don't have strong opinions) about substitutionary atonement who might not be much concerned by the actual manner of Jesus' death.
I think one of the reasons Christian apologists in the modern era focus on the historical method is that it's one of the very few ways to appeal to people who are persuaded by verifiable facts. We cannot summon God as a spiritualist might summon a departed soul. Unfortunately, appeals to reason are also limited to just one facet of the human condition. Even in Jesus' day, knowledge of the truth was not enough.
