Ray has given the first part answer to the question, but OP is waiting for the second part.
This is a really great answer. Unfortunately I phrased my question as
two parts and the responses here are split on what they answer: you
addressed the "other gods are false" part, but quite perfectly. Would
you care to offer some thoughts on the second part, that is, given
that you acknowledge the existence of Satan and other beings like
angels within the bible, on what basis is God a deity and those are
not? (Others have said "because He created them" but there must be
more to it, since other religions/mythologies have gods creating other
I'm now attempting the second part of the answer. Andrew Vit (OP) gave these as examples as other beings to be explained:
The Biblical universe also includes a varied cast of supernatural
characters like Lucifer, Metatron, Archangels, Demons, Seraphim, etc.
Some of these manifest with power in the world and represent the roles
of messengers, warriors, healers, advisers, protectors, troublemakers,
and so on.
As Ray implied in his answer, monotheism is OUR terminology, not the Scripture's terminology. Based on the revelatory data of the Bible, it is WE as modern readers who try to construe the nature of this one deity as well as the nature of the other beings listed above. So the answer to "on what basis is God a deity and those are not" is a matter of OUR definition, not the Bible's. For example, what is the nature of Satan? There is nowhere in the Bible that the nature of Satan is described systematically, since the Bible is not a theology book. There are only sporadic references to Satan such as Genesis (the serpent), Job 1:7, Isaiah 14:2 (morning star), Zechariah 3:1-2 (in a vision), Matthew 4:1 (devil tempting Jesus), Luke 10:18 (Jesus saw Satan fell from heaven), Revelation 12:7-12 (Satan thrown from Heaven), Rev 20:2 (Satan bound for 1000 years), etc. Therefore it is a question of philosophy and theology.
It is a legitimate question, however, but it falls on the theologians / philosophers to come up with a theory that describes:
- the ontological nature of the being (what is it?),
- the etiology of the being (where does it come from? how does it come into being?), and
- the purpose/function of the being (what does it do in the scheme of things? what are its powers?)
Which theology? Andrew specified Christianity. But Christian theology wasn't static. We also need to include new development during the Intertestamental period (aka Second Temple period) covering the period between Malachi and Jesus where a lot of those beings started to populate the apocryphal, pseudepigraphical, and apocalyptic Jewish writings in that period, including the Dead Sea scrolls. Some Greek myths and philosophical influence also need to be considered. New Testament period theology as expressed in the NT books take all those as the background.
So my answer is going to be the mature Christian theology around 11th century. By that time, Christian understanding of God has included following attributes: omniscient (infinite knowledge), omnipotent (unlimited power), omnipresent (present everywhere), transcendent (outside space and time), eternal, etc. Does this being exist? Yes, says St. Anselm, using his famous ontological argument from 1078 which has YET to be conclusively defeated. Because there can only be ONE of this kind of being, then all other beings by definition can only be LESS than God. This then answers your question "On what basis is Christianity classified as monotheistic given the existence of other powerful beings in the Bible". It is monotheistic because there can only be one being that has those attributes (per Anselm's ontological proof).
About the other beings about whom you ask "Why are these not acknowledged as 'gods' or 'lesser gods' like in the pantheons of other religions: how is the nature of their existence different?", the answer is simply: because according to mature Christian theology the only deity worth its salt can only be one. It's a matter of terminology, so Christian theology DOES make a place for angels and demons, but Christian theology would NOT call them gods like Greek mythology, for example, because a Greek god doesn't have all attributes necessary to fit St. Anselm's God. There exists this one being God, said St. Anselm, so logically it follows that all other beings don't fit to be called god.
What are these lesser beings' nature? I would refer you to St. Thomas Aquinas's writings if you accept his theological, philosophical, and scripture interpretation presuppositions. Or other readers may suggest other systems with different presuppositions.