This passage refers to the Millennium. It refers to the future prophecy that has not yet been fulfilled following the second coming of Jesus Christ, and the restoration and glory of Israel to their land.
And it shall come to pass in that day, that the Lord shall set his hand again the second time to recover the remnant of his people, which shall be left, from Assyria, and from Egypt, and from Pathros, and from Cush, and from Elam, and from Shinar, and from Hamath, and from the islands of the sea. Isaiah 11:11
And there shall be an highway for the remnant of his people, which shall be left, from Assyria; like as it was to Israel in the day that he came up out of the land of Egypt. - Isaiah 11:16
Israel will regather at the beginning of the millennium kingdom from Assyria and from other nations, and a highway will stretch from Egypt to Assyria through the land of Israel as a major transportation link.
Israel will also be regathered from Egypt, which will be a prominent nation during the millennial kingdom.
In that day shall there be an altar to the LORD in the midst of the land of Egypt, and a pillar at the border thereof to the LORD. And it shall be for a sign and for a witness unto the LORD of hosts in the land of Egypt - Isaiah 19:19-20
The altar and monument to the Lord spoken of as being in Egypt will most likely be the Great Pyramid of Giza. Zechariah 14:18-19 is a warning to Egypt if they do not keep the Feast of Tabernacles during this time.
In context of the verses you presented, these verses speak of the millennial reign of Jesus Christ that will go beyond the borders of the Promised Land. Both Egypt and Assyria are millennial counterparts to the glory and prominence of Israel.
In the same day the LORD made a covenant with Abram, saying, Unto thy seed have I given this land, from the river of Egypt unto the great river, the river Euphrates - Genesis 15:18
When the Kingdom of Christ is established upon the earth, the people of Egypt will join the peoples of all the nations to worship the God of Israel, meaning that Egypt will be God's people.