There are lots of computer companies besides FAANG, and one of the advantages of attending college near Silicon Valley (e.g. UCB, UCSC, SJSU, Stanford, SCU, and others) is noticing and being noticed by many of the smaller computer companies in the area (versus most of FAANG that recruit everywhere and everyone applies to anyway).
Stanford CS covers a lot of areas: https://cs.stanford.edu/degrees/undergrad/Tracks.shtml . Note the option of designing your own track or choosing an unspecialized track. Game development needs and touches a lot of areas of CS, such as artificial intelligence, graphics, and human-computer interaction, as well as depending on the core CS concepts and knowledge in algorithms / theory, systems, networking, data management, and security. It also involves art, creative writing / storytelling, social sciences, and often physics (i.e. courses that can be chosen for general education or free electives outside of CS). At many colleges where there is not a specific game design track or major, you can choose electives with a CS major relevant to your interest in game design.
Be aware that game companies hire lots of regular CS majors; a game-specific major is not needed. A game-specific major may be limiting if you choose to seek employment outside of the game industry (which is very volatile and some find less than ideal in working conditions compared to other CS-based jobs).