One way to account for this rise is to note that Islamic fundamentalism was a way for Muslims to distinguish themselves from both the communists and the West. This allowed them to create a separate identity for themselves.
During the Cold War, Muslims might not have wanted to side with the West. They would have seen the West as the supporters of Israel and the people who had been the imperial power in the Middle East. At the same time, the communists were aggressively secular. Communism promoted atheism.
Thus, the rise in Islamic fundamentalism can be attributed to a desire on the part of Muslims to reject both sides in the Cold War and maintain their own independence from the superpowers.