I suppose on a flat plain with major roads meeting at equal distances apart, a town might grow organically in a rough circle. And if it's a preplanned town it could be round. And if there is a specific thing in the middle at the centre of town society, earlier forms of the settlement may look round.
But it is going to be mostly dictated by geography and transport routes. The land may not be flat. Buildings will spring up along existing routes such as the major roads and the river, which will become more pronounced as the settlement grows larger. The end result could possibly still be something looking sorta-round though (if the settlement is where a lot of roads meet), but not perfectly so even if that is the case.
These are just my thoughts on the matter anyway.
*edit* On your map it looks like you have four major roads meeting roughly equally apart at the coast. In this case the middle of the settlement is going to look roundish. And the main city walls will look roundish. But then outside of that you will get the outer fauburgs (suburbs basically) that will spring up along those incoming roads and that will start to distort the shape. Those suburbs will be bigger along the more important roads, and along those where it is easier to build.