Firstly, Shaktam is the worship of Mahadevi. Mahadevi is Shakti, the sacred force and power of Consciousness, seen as Shiva. It is Shakti that is responsible for creation preservation, destruction, etc. She is that threw which everything happens.

According to Shaktam this world we live in is indeed real, as opposed by Adi Shankara. The reasoning is quite simple: 1) the world is caused my Adi Shakti who is Aum. 2) Shakti is the power of Brahman and is one with Brahman. 3) the world and Shakti are within Brahman. 4) Brahman is reality, therefore it can only contain reality, only reality is in Brahman. 5) because the world and Shakti are within Brahman, they both must be real.