no, you would theoretically get more us on ur resume if you just work as a swe after undergrad. i think a lot of masters in computer science fields generally aren’t that good (unless it’s like ML because it’s hard to get into without being from a target school, or something interdisciplinary)
definitely do a bachelors in cs, swe is a fake bachelors in theory, and should only really be a concentration / minor. my argument is that you really shouldn’t do masters unless it’s like machine learning, computational biology, hci, and it probably needs to be a “prestigious school” to justify it. do a lot of projects on the side in game dev, join the club, make one if it doesn’t exist, etc… game dev is an art, not something that needs more education, it needs practice. no masters in swe prolly