I recently tried to make sourdough with my starter, it didn't rise. Why is there still a crumb? I started and cared for my first sourdough starter for 6 days, had a decently active starter. It would rise noticeably, maybe 1.3x after feeding.

I made a basic sourdough recipe using my starter. It's obvious that my starter wasn't up to the task based on the picture below. My current hypothesis is that the tap water in Seattle has to much chlorine. I have since restarted with filtered water.

Anyways, I'm wondering why, despite being unleavened, there is still a crumb in the "bread"?

Is it because there was some, but more than zero, fermentation? If so, why didn't the yeast multiply and leaven the whole loaf?
Looking at that picture you did definitely get a rise, in fact you got some big air holes. I would be happy to get that crumb, and I have baked plenty of bread. From the shape of it I suspect that what happened is that it simply spread out on you, rather than going up, which is common with dough that has a high hydration level like yours seems to be. 

Bread dough is a bit like water in that it will flow the path of least resistance, if you simply plop a dough down without restricting it or shaping it you'll get a spread. Shaping will help depending on the result you are looking for, but I would recommend you use a shaping basket, also known as a proofing basket when you do your final rise.