I've combined two previously-posted photos of the building at Hollywood Blvd. and Cherokee Avenue for convenience:
The device seems to be aimed very precisely at some point across the street, seemingly at 6636 Hollywood Blvd. In 1937, 6636 had the offices of the World Wide Wonders Motion Pictures company:
Film Daily Product Guide and Director's Annual of 1937.
Could the device be some sort of screen with an internal projector, meant to be seen from the offices of said company for some purpose (publicity? development of backing?)? Or could it be a projector meant to project something onto that building, again for the purposes of that company?
And so . . . no final answer yet; but the plot thickens with the World Wide Wonders Motion Pictures company.