I am going down the street/road/pitch/square
I am going farther along the street/road/pitch/square
The expression 'down the...' doesn't necessarily have anything to do with the length of your chosen path. Don't think about it in terms of decreasing lengths. It just means that there is a path that extends a distance and you are just going farther along the distance that this path/space extends.
And don't get confused with the 'down' part of it. If you are standing in the middle of a somewhat level road/space/etc and you wanted to go farther along it, you would still be going down the road/space/etc regardless of what direction you are going in.
Take note that this doesn't apply for elevations however. If you were standing at the top of a hill or a road that has a significant slope and you wanted to go towards the bottom, you would be going down the hill/road. But if you were at the bottom and are now going towards the top of the hill/sloping road, you would be going up the hill/road.
My friend wanted to run down the village.
Please take note of @P. E. Dant's comment. It is a completely different expression that means that you want to say bad things about the village.