The scrolling electric sign you describe was described as a motograph by Frank C. Reilly in 1923 (US Patent and Trademark Office). In a patent for a Controller for Electric Signs," Reilly explains:
This invention relates to moving electric signs and more particularly to that type of moving electric sign known as a motograph.
Motograph in this usage(1) may have been coined as a combination of moto- (motion) and -graph (writing) - moving writing. The origin of this usage can be traced back to the collection of Everett H. Bickley, an inventor:
In 1911, Bickley developed and marketed his first commercial invention, the "motograph," which was an electric sign which spelled out moving messages with light bulbs. The first motograph was erected over the Columbian Theatre in Detroit, but others were eventually seen in cities throughout the world. Unfortunately, he sold his interests too soon and made little money from this idea.
Some other usages are possible. Note several appellations used by Dale L. Cressman in an article about the New York Times's own sign, the Zipper:
The New York Times installed an electric "moving letter" sign on its building in Times Square. Popularly known as "the zipper," the monograph drew significant attention from New Yorkers over the next thirty years and contributed to the reorganization of readerships into audiences; it both anticipated television and was eclipsed by it.
Specific products will have various names - LED sign, electric message sign, scrolling ticker - but motograph came first.
(1) Motograph was not original to Bickley. An electromotograph (sometimes shortened to motograph) was invented by Thomas Edison for use in long distance communication. Oxford English Dictionary, "electro-, com. form":
a device invented by Thomas Edison for producing movement of a lever (in a telegraph) or a diaphragm (in a telephone) by utilizing the variation in friction between two conductors in relative motion when the current between them varies