I think people who were raised in a religion often think that belief in a higher power or a "god of one's own understanding" is somehow not religious.
But a god of one's own understanding is still a god. Belief in a a spiritual higher power is a religious belief.
The program does not require one to subscribe to any specific organized religion, but it does expect that in doing the steps one will come to believe and have a spiritual awakening. So the program is religious in that its goal is to develop one's own personal set of spiritual principles.