To understand this quote by Swami Dayananda, you need to sign onto the idea that God is everything, including the body-mind-sense complex (a product of God) and consciousness (the essence of God). Thus, to be "swallowed in the vision of Īśvara [God]" and become one with God, you need only realize this simple point!
See if you can follow the logic (comments in brackets):
"Understanding the kāraṇa-kārya, cause and effect, is the basis of the whole teaching [of Vedanta]. The effect is inseparable from the cause, which is Brahman [pure consciousness]. Therefore, the effect [creation] is inseparable from Brahman. Because it is inseparable, the effect is mithyā; it is only apparent. Therefore, the entire jagat [world] which includes the body-mind-sense complex is a product and is mithyā [apparently real]. So, between the cause and the effect, the relationship is very peculiar. The cause is satya [absolute truth], that which exists independently, and the other, which is mithyā depends upon that independently existent principle. Like pot and clay; like your shirt and its cloth. If you analyse it, the cloth is mithyā, the thread is satya, the thread is mithyā, the fibre is satya, fibres are mithyā, particles are satya. Like this you can go on and on. Then what is satya? That which does not depend upon anything else. Is there such a thing? Yes, that is Brahman. Thus through this kāraṇa-kārya-viveka [discrimination between cause and effect], the teaching takes place here. By knowing that Īśvara [God as the creation principle] is everything, they [devotees] become one with Īśvara. How is that? This second step is interesting. The first step is knowing Īśvara as the maker and the material cause and therefore, that the effect, the creation is non-separate from him. This is the knowledge of Īśvara. Knowing it, you come to recognise you are that Īśvara [as a product of]. This is the second step. If Īśvara is everything, your physical body is Īśvara, your mind is Īśvara and your senses are also Īśvara. What is not Īśvara? If everything that is created is Īśvara, perhaps consciousness is not Īśvara because it is not created. You cannot say that because what was there before creation was sat alone [existence; 'sat' is one of three synonyms for Brahman: sat-cit-ananda (existence-consciousness-limitlessness)]. If consciousness is uncreated, that cannot be different from the sat, the svarūpa [nature] of Īśvara. So, sat [existence] and cit [consciousness] are the same. Knowing Īśvara, you become one with Īśvara. This is not an ordinary statement. First, it is presented as though something else is the cause. Afterwards, if you analyse the whole thing, it ends up that you are the cause [because both God and the individual share the same essence—consciousness]. Your isolation, the separation between the Lord and yourself is simply swallowed in the vision of Īśvara. Therefore, the vision of Īśvara is the vision of yourself, the vision of the whole [because once realized, there is no actual separation]."
—Quote from "Bhagavad Gita Home Study Course - Volume 6" by Swami Dayananda