As Almo says, roles within game development vary from studio to studio, or sometimes even between projects for a single team. But there are common patterns.
I think the next equivalent would be called Creative Director here:
The creative director is responsible for the overall vision of the
Product: gameplay, visual style, story, audio assets, kinematics and
Marketing materials. This person is often the creator of the game
Concept and can serve as the main designer. He or she works under
the supervision of the producer and is responsible for leading the teams
by artists, designers and programmers who interact directly with them
senior managers of each department.