I think what I see here is the very real fact that we are talking in 2016 understanding to a question that is asking about BC understanding and scripture's application. The question is what is monotheism? This is a good question. Monotheism speaks to two things, the oneness of God and/or the belief in only one God. It doesn't address the reality of there being one god or any criterion for an ultimate determination to the truth of God; only the belief in one god.
I see others have spent time addressing the belief in one God by establishing the criterion for determining the truth and reality but not so much addressing what the word means in accordance to scripture. Let's step back in time as best as we can to Moses. The question Moses asks will shed light on exactly what you are asking.
Exodus 3:13 And Moses said unto God, Behold, when I come unto the children of Israel, and shall say unto them, The God of your fathers hath sent me unto you; and they shall say to me, What is his name? what shall I say unto them?
This question, supports the notion that the Israelite in Egypt believed in multiple gods. Moses was educated but yet wanted a way to distinguish God to the Israelite by asking for a name.
Exodus 3:14 And God said unto Moses, I Am That I Am: and he said, Thus shalt thou say unto the children of Israel, I Am hath sent me unto you. And God said moreover unto Moses, Thus shalt thou say unto the children of Israel, the Lord God of your fathers, the God of Abraham, the God of Isaac, and the God of Jacob, hath sent me unto you: this is my name for ever, and this is my memorial unto all generations.
It would be quite silly for us to jump to the modern understanding and say the biblical use of gods referred to ONLY handcrafted idols. The Israelite at that time, did not believe in only one god, this is a very polytheistic environment. They were essentially accustomed to the pantheon idea in Egypt and in the surrounding regions. They were also accustomed to displays which showed one god superior to another. This wasn't always the case and was an interesting phenomenon for Moses.
Let's now step back as best we can to Abraham 400+ more years. At this time we can see that the Egyptian at that time knew God and didn't need distinctions based on the interactions between Abram and Pharaoh. We can infer that there was an understanding of monotheism in Egypt before the polytheism. Canaan was probably accustomed to polytheism since we can see Laban's daughters already dealing with idols.
Staying with Egypt if we fast forward just a bit. When Joseph entered Egypt this monotheism idea didn't seem foreign to them also, in fact in speaking to Potiphars wife he says,
Genesis 39:9 "There is no one greater in this house than I, and he has withheld nothing from me except you, because you are his wife. How then could I do this great evil, and sin against God?" (Gen 39:9 NAS) Again, no distinction was needed.
Something happened between the time of Joseph (before slavery) to the time Moses was in Egypt that brought forth an idea or maybe a reality of multiple inferior gods similar to Canaan which we ought to treat as real, even if the idea is ludicrous to us now, it was real to them then.
God even recognizes this state of affairs as you pointed out. We see this strongly in his final plague. Exodus 12:12 'For I will go through the land of Egypt on that night, and will strike down all the first-born in the land of Egypt, both man and beast; and against all the gods of Egypt I will execute judgments-- I am the LORD. (Exo 12:12 NAS)
This issue was enough for God to cut it out with the very first commandment. Do not bring these inferior beings into my presence or set them before me, or fear them over me is essentially what that verse communicates. Yes, we see idolatry with the graven images becoming more frequent and that is addressed in the second commandment.
God goes through feat after feat establishing his supremacy and legitimacy as the only worthy of the title of God, we describe these as the attributes of God. Unlike the other gods which were fragmented and competing, ever changing and constantly shown up, God expressed in 3 persons of the trinity was of one accord.
We could speculate as to what these other gods are, some scholars propose fallen angels or demons, some go as far as satan. In our day and time, I suppose it means less since we can verify the truth that there is only one God.
