What would be a good first choice to teach game programming to beginners? In my institution we are close to starting a new graduate level program for game development. However, this program will accept non-digital game designers or other non-experts (real architects who are into interactive design), too. Therefore, the programming course must cover inexperienced programmers (an introductory course for adults who have bachelor's). At the same time, it is preferable if it also includes tools for expert programmers who may also have bachelor's in computer science (this part is optional).

The program is designed to be generic. So, some people may prefer to come up with 3D games using an engine, while others prefer to instantiate board games for children. As you may see, programming is not the aim as in CS courses, but just another tool, here.

What language might be a good choice to teach inexperienced programming in the game domain?
For those interested in 3D (though, it can be used in 2D) game making with an engine, I would suggest teaching Unity. It's an engine and a platform for creating games. 

Unity can be used with C# and Javascript, which means that those who choose to use it will also have some experience with some very popular high-level programming languages. 

Additionally, Unity is, in part, a graphical engine. This means that the game is made in a graphical way, and the student can decide how much coding would be involved (Unity has an asset store, in which some scripts can be used. Some are free and others are not). This allows students to be comfortable with the game they are making, and they decide how much programming they do. This
 degree of freedom is often very beneficial for students.

A portion of making a game in unity involves designing, and artistic work. This can be a very convenient environment for the students who are into interactive design. 

Overall, Unity fits the bill by being flexible and answering each students needs and areas of interests and expertise. So I think that it is a very good choice to start with. 

From my experience, it's quite enjoyable to make games with it just for the sake of playing around with the software. This isn't too relevant to the question, but students who enjoy working on projects are more likely to make great projects.