I'd like to make three preliminary points, then answer the original question.
First, a passage that was not mentioned commands the Israelites to completely destroy fellow Jews, should they turn to idolatry:
12“If you hear someone in one of your cities, which the Lord your God gives you to dwell in, saying, 13‘Corrupt men have gone out from among you and enticed the inhabitants of their city, saying, “Let us go and serve other gods”’—which you have not known— 14then you shall inquire, search out, and ask diligently. And if it is indeed true and certain that such an abomination was committed among you, 15you shall surely strike the inhabitants of that city with the edge of the sword, utterly destroying it, all that is in it and its livestock—with the edge of the sword." [Dt 13:12-15]
Thus, that the intent of the commandment for total destruction was not against a particular people, but against idolatrous religion and culture. So I must take issue with the use of the word genocide in reference to these passages, a word which is quite universally understood as indefensible and immoral in the highest degree, indicating "crimes against humanity." Such a highly flammable word cannot be rightly drawn out from the passage (though it can easily be read into it). The destruction was judgment upon sin, not presenting them as an offering to God (for they were anything but holy), and not a wanton act of genocide.
Secondly, Deuteronomy is presented by the writer as history, and treating it as such is the right approach, over against speculating about what the ancient writer might not be telling us, what facts he omitted, or possible motives of the writer which are nowhere to be found in the text itself. The heart of the Judeo-Christian religion(s) is not theories about God and men, but historical facts. To undermine these based on cynical modern assumptions is not honest interpretation of scripture, but simply demolishing it.
Thirdly, I am altogether in agreement with the suggestion that the real task at hand isn't defining the words, but getting at the intention of the original writers. The trouble is, their intention can never be discovered empirically and conclusively, other than by interpreting the text and context. In this case, the intention is either to record the history (as is plain and obvious). Rejecting that, suggest any motive you please, but don't suggest that it is anything more than an eisegetical theory.
And so, to answer the question with the assumption of scriptural inerrancy: the OT writer was right and honest and forthcoming with all the details; "completely destroy" meant to kill every living creature; and it was God who declared this complete and total judgment against the idolatrous nations in Canaan, including any Jewish community which should stray into idolatry.
Again, from the point of view of inerrancy, the Scriptures are not in question. What is in question is the character of God, God's right to doom entire nations, and the justice of that complete destruction. This is where the inerrancy advocate has the most difficulty, the way things are today, and is likely the real motivation behind the OP's question.
A humanist may proclaim that God has no right to doom entire nations, or that God couldn't have possibly commanded such a thing. But he cannot infer this from the Scriptures. A textual-critic may dismiss this or that passage, but that's just avoiding the text rather than interpreting it.
The assumption of inerrancy makes ones interpretation dependent on the Scripture itself with the presumption of belief. Is God in the right if He destroys a nation, or commands his people to do so, or floods the entire world, or sends his own people into slavery? We can only approach sort questions with logic that comes from faith, credo ut intelligam, to use Augustine's formula.
Is inerrancy an assumption that is incompatible with interpretation of scripture? Only if the viewpoint of faith in God is incompatible with scripture. Inerrancy demands faith, and such faith strengthens logic.
A logic that justifies God is called a theodicy. Is theodicy a hermeneutical method? Yes, in this case it was exactly Moses' own method of interpreting God's actions in Deuteronomy:
"He is the Rock, His work is perfect; All His ways are justice, A God of truth and without injustice; Righteous and upright is He." [Deut 32:4]