The cartoonist may also have been concerned about the political power and corruption of the railroad companies.  In the mid-1880s, competition from the elevated railroads led the owners of horse-car companies to desperate measures, including bribing state legislators and city aldermen.  In particular, a conflict developed between Jacob Sharp's Broadway and Seventh Avenue Railroad and the New York Cable Railway Company (neither company's trains were elevated).  Allegations of massive bribery and a subsequent trial were major news stories during 1885 and 1886.  

The struggle between horse-car and cable-car companies left the elevated railroad companies in an even stronger economic position.  In the cartoon's background, the flags on the building are flown as they would be on a (pirate) ship, and the middle flag (click to enlarge the picture) appears to be an octopus--a symbol commonly used to denote the grasping, omnipresent power of business monopolies.  The train's route around the Statue of Liberty may not suggest (only) a roller coaster, but the liberty of the people being encircled and constrained by the might of the elevated railroad companies.

Another possible source of artistic inspiration for this cartoon was an inquiry by a committee of the New York State Legislature into corruption charges against John Y. McKane, the police chief and political boss of Coney Island.  In 1869, McKane was elected city commissioner of Gravesend, and he developed properties in Brighton Beach and Manhattan Beach (all of which are part of the Coney Island community).  In 1881, his associates in the state legislature pushed through a law establishing a police force for Coney Island separate from Brooklyn's, and McKane was elected to the unsalaried position.  McKane collected a percentage of the fees for licenses that he issued to the gambling houses, saloons, concession stands, and other businesses on Coney Island.  He became a major political player in Brooklyn and state politics, and helped carry the state (and thus the election) in 1884 for Grover Cleveland, the Democratic presidential nominee.

McKane was careful not to leave a trail of evidence and to deny all knowledge of wrongdoing.  In the spring of 1887, however, a railroad executive testified before a committee of the New York State Legislature that McKane had paid him a $4000 bribe to facilitate the political boss's purchase of some real estate from the railroad company.  George Tilyou, the son of a prominent Coney Island real estate broker, took the stand against McKane.  Tilyou reported the political boss's involvement in schemes of kickbacks, bribery, and fraud, identifying specific individuals and places.