score:8
There are two solutions, neither of which are immediately obvious on Google Maps or ... on anything at all. If you continue walking on South Jackson almost immediately after the little plaza there is a modern office building and you actually can turn left and kind of sneak next to the building on a walkway and then walk down the stairs to the station entrance. https://goo.gl/maps/hFmzyqG3qnZBiyos7 the clock tower is the station. That's your goal. Especially in the dark (when the train leaves for Vancouver...) finding this without prior knowledge is impossible, it really looks like it only leads to the side entrance to the office building. But no, there are stairs...
There is another way, close to the south end of the Link station, this I discovered from several Tripadvisor posts: there is a walk path called Weller Street Walk continuing on Weller Street Bridge and at the end of the bridge you have an elevator down to the station entrance. At least the Weller Street Bridge has a glaring big King Street Station sign on it -- it's a whole another question of how on earth would anyone end up there unless they already knew where it leads. Here's how to find Weller Street Walk from the Link Station:
Although this little map was published on the occassion of a temporary closing of a Sounder only entrance, it is actually a walking map to King Street Station: