So, as I understand it, the sentence says that the river flows across the horizontal (axis?) of the street. Is that correct? I'm really confused by this way of expressing that A crosses B. Since it feels very complicated and unnatural to me, I'm afraid that I don't understand it correctly, even more so because in context of the dialogue, they don't really pick up that information further down.
This also poses a problem for me because を appears in a function I didn't really encounter so far.
When used in context of directions, I found it as a marker for going along something "道を行く" or inside of something "公園を散歩する", sometimes also in the function of crossing something like 交差点を渡る。 But this feels like a mix because its like going along the horizontal of the street.