Coral Gables is a perfect example of the "shotgun house", a very frequently used house design in New Orleans. The long and narrow design fits the narrow but deep city lots. By creating lots of this shape, city planners were able to get the most use out of the usable land in an urban landscape with more water than land.
In New Orleans, you can find many different versions of this house from various time periods. Each time period will have its own design features and flourishes. No matter if it was built for a rich or poor family, the basic underlying structure is the same.
If you look up "right little, tight little" shotgun house in the dictionary, this house could be the accompanying image.
You can read more about the history of the shotgun house in New Orleans in this article by Richard Campanella on Nola.com.