Why is Christianity considered a monotheistic religion? One of the commandments states "place no other gods before me". Does this mean God is implying the existence of other gods, or why is this explicitly stated?

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. 

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?

On what basis is Christianity classified as monotheistic given the existence of other powerful beings in the Bible?
Christianity is monotheistic as its adherents believe in only one God.

The first commandment speaks about the gods of other religions. Although Christians believe in only God, they do acknowledge that other gods are believed in by non-Christians.

In other words, there are many gods in which to believe, but you believe in only one if you are Christian.

Also, the same passage applies to Muslims and Jews.

To answer the third part of your question: the belief in the Christian God (i.e. the Trinity) is what defines Christians. 

Belief (or lack thereof) in the supernatural attributes of Satan, the Saints, Virgin Mary, angels vary by interpretation, but in general these figures are considered non-divine, and certainly subsidiary to God.