It is very simple. For example, when I buy an I-Pod, I use it to enjoy the I-Pod by listening to music. Therefore the root of enjoyment is possession of the object.
Similarly if God is the Supreme enjoyer, it simply means our body, mind, senses and all of sense objects (entire material nature) belongs to God. He is therefore the supreme possessor of all objects and the supreme enjoyer. The problem arises when we (jivatmas) who are part and parcel of Him assume (this is Maya) to be Him and treat all objects as objects of our enjoyment. This illusion of mistaken ownership (which by the way arouse from envy) is the cause of misery to the Jivatmas. All we have to do is change this mentality and give back the ownership to the right owner which means use His (God) objects (includes this body, mind and senses) for His enjoyment. This way God, jivatmas and His energy (Maya shakti) will be in perfect harmony!