the article says the casino was the Casino des Grottes Rouges (Red Caves Casino in French) It would be Grotte Rossa in Italian, so I'll bet they were seeking to attract French from the French Riviera - Côte d'Azur - to come a few miles across the border by using a French name.

The geographic formation is Balzi Rossi, which translates to "Red Caves" in the Ligurian language (a/k/a Genoese, spoken in that region in France, Italy and Monaco)

and Ventimiglia is the town in which this area is located