First of all, you can ignore the “bachelor of arts” vs “bachelor of science”. The “arts” is short for “liberal arts and sciences,” and comes from a Latin word that means “art or principled practice.” It’s not visual or creative art, and you don’t need to be creative to get one. You can get a BA in physics, chemistry, computer science, biology, etc. at some colleges. The letters of your actual degree - BA or BS - don’t actually matter; what matters are the classes you took and the skills you learned in them. There’s no ‘stigma’ towards a BA.
Interactive design, however, does require creativity. Are you just afraid that you are not creative enough, or have you actually received feedback to that effect? You are right in that the gaming industry is difficult to break into, and while you don’t technically have to be a gamer or into gaming per se to get a job, there are still a lot of studios and gaming companies that prefer to hire people who are ‘into’ gaming. That’s beginning to change a little bit, but there really are roles for which understanding games (broadly - you don’t have to play first-person shooters, but some kind of interactive experience) is really important. (I work in the video games industry myself.)
But there are lots of other things that entertain others - books, movies, television, music, etc. And there are jobs to be had in technology across all of those fields. For example, there are products like Spotify and Apple Music; there are ones like Hulu, Netflix, Amazon Video; there are companies like Warner, Disney Interactive, and Turner Broadcasting; there are monitoring firms like Nielsen or NPD; there are actual movie production companies that use technology, like Pixar or Dreamworks; there are technical book-related positions at companies like Barnes & Noble, OverDrive, Zinio, and Audible (now owned by Amazon).
Experience architecture is essentially the field I work in. MSU’s program is one of the only bachelor’s level programs like this, but the area is actually a pretty interesting and potentially lucrative one. Almost all tech companies hire people who work on user experience (UX) and user interfaces (UI) in different roles: I’m a researcher, but there are also designers, project/program managers, artists, and software developers who concentrate on the UX/UI of products and services. The XA degree at MSU seems to teach you a little bit of all of those fields, and you can probably choose to develop deeper competencies in one or two of them.
Computer science is a classic degree for doing development or even interaction design. Most of the designers I work with have design-related degrees, but a relatively large minority have degrees in computer science (usually with some supplemental work in art and design).
It’s also potentially possible to double major in them both, or to major in one and minor in the other. Which one you choose will depend on your interests and goals.