Does Matthew 7:13-14 picturize an actual geographical entity of Jesus' time?
The facile answer is yes.
Gates and doors have existed in civilized societies for millennia. Their primary purposes have been to provide and prevent access. Gates and doors are security devices, allowing key-holders in and non-key-holders out. The gates to a city, of course, are larger and much more secure than the gate to a garden or a park.
In Jesus's day, and before, the gates of a city offered a measure of security for city dwellers, and perhaps more important, they were the meeting place of the elders and judges of the city when important issues needed to be discussed and decisions made. In essence, the gates of the city represented, symbolically, the political power vested in the city's leadership. These representatives of the people safeguarded the moral and ethical values espoused by the community.
Jesus used that symbolic imagery in his response to Peter's confession:
Blessed art thou, Simon Barjona: for flesh and blood hath not revealed
it unto thee, but my Father which is in heaven.
And I say also unto thee, That thou art Peter, and upon this rock I
will build my church; and the gates of hell shall not prevail against
it (Matthew 16:17-18 KJV, my emphasis).
In other words, all the power and machinations of Satan and his emissaries would ultimately be defeated by the Church of Jesus Christ.
Picture, if you will, two different cities and two different gates to those cities. One city gate is touted as the easiest to enter, and it opens to the widest and most beautiful walkway. It has flowers, trees, benches, lamp lights, drinking fountains, restrooms(!), and maybe even some hotdog- and Italian ice vendors.
The other city gate is not touted at all. In fact, many people avoid it because they think it provides entrance into a nondescript path with very little street appeal. No restrooms, no flowers or trees, no conveniences to speak of, just a narrow sidewalk with no benches on which to sit in order to rest sore and weary feet. And no hot dogs!
I think you know where I am going with my little analogy. The first gate and path--the highly touted one--represents the entrance and the path to another city, the City of Destruction. Satan and his minions do their best to make it seem attractive, pleasurable, and filled with the creme de la creme of society--the smart and beautiful people. The apostle John called these attractions the lust of the flesh, the lust of the eyes, and the pride of life.
Virtually everyone knows about each gate and path. The much touted gate and path has an army of demons who have been schooled in the art of temptation. They are practiced in offering gullible people the bitter-sweets of life in the guise of something that is only sweet and desirable.
The other gate and path has its handbook for life, the Bible, and it has a community of faith (the Church universal and various local churches) in which the people who choose to enter the path of life are welcomed, accepted, and loved.
When local churches are functioning as they should, members reach out to people on the wrong path, encouraging them to repent and find forgiveness and peace with God. The insiders encourage the outsiders to join them in experiencing the more abundant life that is found in a relationship with God and with his people, all of whom are sinners saved by God's grace. The ground is truly level at the cross of Christ.
In short, Jesus was not referring to any particular gate and path in his teaching. As with many of his teachings he used metaphors, analogies, and similes that included familiar, common, even universal things and people. Jesus himself, of course, was the way (and the truth and the life), but he was also the door to the sheep fold, the bread of life, the good shepherd, the living water, the true vine, the light of the world, and the resurrection and the life.