This but DotA 2 for me. 6000+ hours and I'm still trash.
Yep that's the one. If you can make a cron job to make the zip file, logrotate could handle keeping the last x files.
It might sound complicated, but the cool thing about *nix environments is that everything is made up of a combo of little tools. You can learn one at a time and slowly build something super complicated over time. First thing would be figuring out the right set of commands to make a zip file from the directory I reckon. Then add that to cron so it happens every day. Then add logrotate into the mix and have that do its thing every day after the backup runs.
Sounds like a job for logrotate. It does more than just log files, kinda average name I guess. Checkout this server fault q&a for more details. https://serverfault.com/questions/196843/logrotate-rotating-non-log-files
I'm old. I've been playing Dota2 as my primary game since 2012. It works out to about 500 hours a year or so, which is still a lot but yeah.