Parece que George R. R. Martin mudou de idéia para a localização do Portão da Lama depois de escrever A Game of Thrones. Isso é feito em backup, pois o parágrafo antes da segunda citação no OP diz que a margem do rio está a caminho do Portão da Lama não depois dela.
A gull wheeled overhead as she made her way down the hill toward Flea Bottom. Arya glanced at it thoughtfully, but it was well beyond the reach of her stick. It made her think of the sea. Maybe that was the way out. Old Nan used to tell stories of boys who stowed away on trading galleys and sailed off into all kinds of adventures. Maybe Arya could do that too. She decided to visit the riverfront. It was on the way to the Mud Gate anyway, and she hadn't checked that one today.
The wharfs were oddly quiet when Arya got there. ...
A Game of Thrones, Arya V
Eu também twittou Elio e Linda, os co-autores de O Mundo do Gelo e do Fogo, e eles responderam com o mesmo raciocínio que eu acima. (Eu suponho que eles obtiveram suas informações do mesmo texto que eu e não de qualquer coisa extra que eles tenham acesso).
O ponto estendido de Elio e Linda fica claro em A Clash of Kings, quando o texto descreve a beira do rio como estando do lado de fora do Portão da Lama.@CarrotLethal: Hello! In AGoT how does Arya get through the Mud Gate? It was only open to those entering the city but Arya manages to get through it to the wharfs and fish market. Any ideas? Thanks!
@westerosorg: GRRM's conception of the Mud Gate changed between AGoT and ACoK is, I think, the answer. In AGoT, Arya goes to the riverfront because "its on the way" to the Mud Gate, whereas with ACoK the Mud Gate is "on the way" to the riverfront.
Beyond the castle, King's Landing rose on its hills behind the encircling walls. The riverfront was a blackened desolation; the Lannisters had burned everything and pulled back within the Mud Gate. The charred spars of sunken hulks sat in the shallows, forbidding access to the long stone quays. We shall have no landing there. He could see the tops of three huge trebuchets behind the Mud Gate. High on Visenya's Hill, sunlight blazed off the seven crystal towers of the Great Sept of Baelor.
A Clash of Kings, Davos III
O mapa no ACoK agora corresponde ao que está nas Terras de Gelo e Fogo para a localização do Portão da Lama à beira do rio. (Note que somente os mapas nas Terras de Gelo e Fogo são canônicos, mas neste caso eles combinam e mostram o processo de pensamento de George mudando entre os livros.)
As Terras de Gelo e Fogo, Mapa de aterragem do rei (cortadas)