Unfortunately, Google does care about the design. The problem is that a lot of sites were thrown up in the old days of the web and got a lot of links. They just stayed in the search results forever and ever without adding anything valuable today because they had a ton of backlinks. One way Google got rid of them was to target sites with old designs. It looks like you have a separate html page for every review, so it's easy for the googlebot to flag that.

Basically, your site got caught in the crossfire from other older sites sucking. It's fixable. And, definitely get those DMCAs out.