I would bet that 95% of Google SWEs have heard of the Game of Life, but you can be an exceptionally good software engineer without that knowledge. It's usually considered recreational mathematics, which is a small or non-existent part of most core university CS curriculums, and not everyone in the field explores such topics outside of their formal work or studies.

Also, their interview process is usually not 3 months. Most engineers have a 45-minute phone interview or two, followed by a day of onsite interviews lasting 4-5 hours.