If we accept that learning art will help you to communicate with artists, then learning some computer science should help you communicate with programmers.
Intro to Programming. Some aspects of game design are pretty technical; if game data or rules are stored in a scripting language (either a commercial one like Python or Lua, or a proprietary one) then it is often expected that a designer will be creating content in those languages, which requires at least some fundamental knowledge of programming. Since you do want a solid foundation, take the course for CS majors if they'll let you.
Data Structures and Algorithms. I don’t feel that a single, introductory programming course is enough to truly understand how to convert ideas into code. A course dedicated to algorithms will give you a better idea of how that’s done, and a course dedicated to data structures will give you some tools that’ll make certain problems much easier.