What would be considered the “best” major for someone who wants to become a programmer, specifically a video game programmer or designer?
Video game programmer and designer are two very different jobs that require very different educational backgrounds. a programmer would require a computer science degree, some universities offer a specialization in video games. A video game designer would require a more arts-oriented interactive media or design degree.
I’d suggest you look up a job posting on monster/indeed/job search website to see what educational backgrounds are required for the type of job you’re interested in.
I work in video games myself.
Computer science is the best major if you want to be a video game developer (software engineer/developer).
Designers have a lot of different kinds of backgrounds…most have more arts-oriented backgrounds but some don’t. I work on a major AAA game and the designers I work with have diverse backgrounds. Most are at least tangentially related to design/art/interactive media, though.