There's a Westworld video game
But…
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.
Westworld is due out on Android and iOS in April but you can sign up to try and get in early if you like.