Possible to make a subdirectory that loops through a single category?

You can create a separate category template for just that one category. If your category’s slug is reviews you can make a copy of your category template and save it as category-reviews.php.

See the Category Templates page on Codex for more info about the template hierarchy.

This still leaves you with the /category/ part in the permalink, which you can either change to something else globally in the permalink settings, or you can maybe create a custom rewrite rule just for that category.