From John Stott, The Message of Romans, p. 130.
“To our initial astonishment, Paul portrays God’s promise as being that Abraham would be heir of the world (Rom. 4:13). Yet in the Genesis text Abraham was promised Canaan, ‘north, south, east and west’ of where he was standing, whose boundaries were later delineated.
How then did ‘the land’ become ‘the world’?
It is partly that, as a general principle, the fulfilment of biblical prophecy has always transcended the categories in which it was originally given. It is partly that God made the subsidiary promise that through Abraham’s innumerable posterity ‘all nations on earth’ would be blessed…
The third reason for Paul’s statement that Abraham would inherit ‘the world’ is surely messianic. As soon as Abraham’s seed was identified as the Messiah (Gal. 3:16; cf. Jn. 8:56), it was further acknowledged that he would exercise a universal dominion (e.g. Ps. 2:8; Is. 9:7).
Further, his people are his fellow heirs, which is why the meek will inherit the earth (Matt. 5:5), and why in and through Christ ‘all things are ours,’ including ‘the world’ (1 Cor. 3:21ff).”