A Thrill a Minute: 1911

IMDB description for the silent film "Jack Fat and Jim Slim at Coney Island," released December 1910: "Most of the attractions at Luna Park involved flinging the patrons across whirling discs or revolving walls; in our modern litigious era, such attractions are unimaginable. One comparatively modest attraction which we see here is the Cake Walk: basically a moving staircase, with two halves moving independently. We see an attractive young girl negotiating this easily."

Cakewalk attractions are still very popular on fairgrounds in the Netherlands.

From "Coney Island - Luna Park":

Theophilus Van Kennel's Witching Waves installed at Luna in 1907 consisted of large oval course with a flexible metal floor. By using a system of reciprocating levers beneath the floor, the ride generated a continuous wave-like motion, followed by another in the flexible floor without the actual floor moving forward. Steerable small cars seating two passengers were propelled forward by the undulating floor. It was fascinating to watch and a popular fun ride.

Looks like the "Sinking of the Maine" ride in the background.
http://www.westland.net/coneyisland/articles/ridelist.htm

I believe the typical cakewalk amusement park ride consisted of a walkway with floor panels that moved in different directions, forward and backward, side to side, up and down, and even rotating, making forward progress difficult and amusing.

From a history of the cakewalk:

The cakewalk was named after a dance which was in vogue at the time. The mechanism consisted of undulating bridges and gangways driven by cranks, The driving belt was often connected to the organ which meant that a speed up of the music meant a speed up of the ride and a speed up of the riders jerking on the bridges.