The world may be a place of confinement for the devils, in some sense, but it is primarily a place created for humans and for the glory of God. Perhaps your question was partly inspired by the famous lines from Marlowe's Faustus,
FAUSTUS: Where are you damn'd?
MEPHISTOPHELES: In hell.
FAUSTUS: How comes it then, that thou art out of hell?
MEPHISTOPHELES: Why, this is hell; nor am I out of it:
Think'st thou that I, that saw the face of God,
And tasted the eternal joys of heaven,
Am not tormented with ten thousand hells
In being depriv'd of everlasting bliss?
Hell as separation from God is a very common and orthodox concept. Thomas Aquinas (Summa Theologica 1.64.4 ad 3), in the same way, says "Although the demons are not actually bound within the fire of hell while they are in this dark atmosphere, nevertheless their punishment is none the less; because they know that such confinement is their due." (Daemones licet non actu alligentur gehennali igni, dum sunt in aere isto caliginoso, tamen ex hoc ipso quod sciunt illam alligationem sibi deberi, eorum poena non diminuitur.) This reference to the "dark atmosphere" follows Augustine, after Paul in Ephesians 2:2 and 6:12.
However, Earth is certainly not identical with Hell. The various narratives of creation present the universe as a place formed and hallowed by God: it is "very good" in his sight (Genesis 1:31) and it is a home for humans and other creatures (see Psalm 104 for extended praise of God's handiwork and sovereign care). John proclaims that God "became flesh and lived among us" (John 1:14), literally "pitched his tent", as part of a constant Biblical theme of God choosing to become known in the world and making it "his" place. The preaching of Jesus is also full of positive references to the Earth's inhabitants, as in Matthew 6:26-29, from the Sermon on the Mount:
Look at the birds of the air; they neither sow nor reap nor gather into barns, and yet your heavenly Father feeds them. Are you not of more value than they? And can any of you by worrying add a single hour to your span of life? And why do you worry about clothing? Consider the lilies of the field, how they grow; they neither toil nor spin, yet I tell you, even Solomon in all his glory was not clothed like one of these.
An Earth which contains birds and lilies, beloved in their own way by God, is not a prison for devils. At other times, Jesus speaks of the world as a place occupied by evil powers:
"Now is the judgment of this world; now the ruler of this world will be driven out." (John 12:31)
"I will no longer talk much with you, for the ruler of this world is coming. He has no power over me; but I do as the Father has commanded me, so that the world may know that I love the Father." (John 14:30-31)
The world does not rightly belong to the present "ruler of this world", but to God; Jesus came to liberate us from the lordship of evil. The Revelation culminates in "a new heaven and a new earth" (21:1), distinct from Hell which is thrown into "the lake of fire" (20:14). The new Earth is not an improved prison, but a new and better home for God and us: "The home of God is among mortals. He will dwell with them; they will be his peoples, and God himself will be with them" (21:3).
(All Biblical quotations are from the NRSV.)