The term "dark ride" traditionally meant a small car traveling along a busbar ride system past simple sets, usually set in the dark and lit with black-light fixtures to give the sets more dimension. They were a staple of Disneyland's Fantasyland in the 1950's, and have been included in at least one form in all the Fantasyland's built since then.
A "dark ride" in the traditional sense is Snow White, or Mr. Toad, or Peter Pan. A newer 21st century dark ride would be Winnie The Pooh on either coast, or Monsters Inc. in California. Even with the newer dark rides, they still don't use animatronics, but rather very simple manequins with only basic movements. Fantasyland dark rides required a B or C Ticket at either Disneyland or Magic Kingdom.
The Little Mermaid falls into a different category. It's bigger, bolder, on a much grander scale, using advanced animatronics and cutting edge special effectsThe Little Mermaid is bigger and bolder than Buzz Lightyear Space Ranger Spin, but not quite on the scale of Haunted Mansion, mostly thanks to its scale and special effects. Although, at Disneyland at least, they have been upgrading the effects used on the older classic dark rides lately. Fiber optics in Disneyland's Peter Pan, digital projections on Alice In Wonderland, or the exciting new "digital mapping" imaging technique added last year to Snow White's Scary Adventures in Disneyland.
Using the traditional definition of a "dark ride", Magic Kingdom's Fantasyland will have only two of them left when Snow White's Scary Adventures closes next year.