The Rook GOLEM is an improved version of the basic Pawn GOLEM. It is most likely the second GOLEMANMC encountered and proves to be fairly dangerous. What has changed from the Pawn model is that it can charge up a special device that can inflict Silence on Aya, preventing her from casting spells for some time. Also they are more conservative with their grenade shots, firing it in 3 shot bursts instead of a full salvo. Also the shield that it has absorbs all damage until it is destroyed.
It is important to understand how a Rook fights in order to help deal with them. Their grenade attacks, much like those of the Pawn can damage others and, since it is possible to see where the grenades will land (via the laser sight) they can be lured into targeting their allies and deal really good damage. The shield can be destroyed with enough damage although this is frequently a waste of ammo. They use the shield when they are charging their Silence inflicting attack and using their grenade launcher. However when they are reloading, they are vulnerable. Their backs are not really well armored so it is not that easy to damage them. While they don't have a lot more HP than the Pawn, they are more dangerous and ultimately can be taken out with similar tactics.