Saddle up, cowboy, there's a Westworld video game. But I'm afraid, yes, it's a mobile game.
It's an official by-Warner-Bros. thing and it's very much in the vein of Fallout Shelter, a management sim and a very popular one at that. You play a trainee employee working for the Delos company, making and maintaining the Wild West theme park above you from a many-roomed underground base. You will build and manage new park locations, build and manage the AI hosts in them, and take care of the guests enjoying them.