Can Buddhism be fundamentalist? Is it fundamentalism if Buddhists believe Buddha's path is the only path, and that all other spiritual traditions or sects are false? And if so, does it exist much in Buddhism?

By fundamentalism, I mean a person believing that their path is the only path, for them and others who believe like them.

I.e. can a Buddhist see another spiritual tradition as valid, even if it is not Buddhism? Such as an agnostic or a mystic from that tradition?
Let's put it this way - a Buddhist is a person who has taken refuge to the three jewels, follows and walks the path taught by the Buddha. Those who do not, are obviously not Buddhists already, rendering your question un-applicable.

Having said that, Buddhist respect other traditions as long as they do not violate the five precepts, and acknowledges that if other paths do not end "true-suffering", then they are not to be pursued.