Rotate the screen as shown above and the girl becomes normal and it's the world around her that's askew. If she dropped an apple it would roll down the hill to screen left. Interesting, eh? I envision a city built on a steep hillside where people learn from childhood how to walk the way the girl's walking here.
No doubt the inhabitants of such a town would travel horizontally most of the time. Going up or down would require too much energy.
Now put aside the concept of a diagonal city, and imagine a normal city where everybody danced to where they were going rather than walked. Of course high energy dances like the Lindy Hop (above) or Hip Hop wouldn't be very practical for distance dancing. For that, you'd need something less strenuous, something like....
...like the Peabody or the Madison (above).
Or the "Wild and Crazy Guys" walk from Saturday Night Live.
I imagine that walkers would think of lots of variations to make the walk dances more interesting.
Haw! A good dance/walk (above) is a thing of beauty!
In such a world what would happen if a boy and girl met on the street?
Well, I guess they'd dance in place while they spoke to each other.
After speaking they'd say good-bye and take off in opposite directions (above, left)...or they'd dance together in the same direction (above, right).
If they needed to stop and talk for a minute they'd go back to dancing in place.