Does dry cat food clean cats' teeth?

No, not really. The idea behind the belief that dry cat food can clean a cat's teeth is that being dry it has an abrasive quality that cleans the teeth like a toothbrush. The mechanical abrasion theory is based on the shape, texture and fiber alignment of the dry kibble.

Apparently dry cat food does reduce the build up of plaque and calculus but in a limited way.

The action is limited because the kibble is normally broken by the tip of the tooth and so does not have any abrasive action at the place where periodontal disease takes place: the line where the gums surround the teeth (gingival margin). Periodontal disease (gum disease in layperson's terms) in cats and dogs is one the most common health problems for these companion animals.

Also dry cat food is high in carbohydrates. That surely is not good for teeth health.

Plaque: soft and colorless. A mixture of food particles, organic and inorganic material and bacteria.
Calculus: also called tartar. Hardened plaque. Mixture of calcium phosphate and carbonate with organic material¹.

Note: 1. Cat Owner's Home Veterinary Handbook

Associated: Picture of cat with gingivitis.