Well that's a crock of shit. Minimum contribution? The fuck does that even mean?
Means that if you worked only for a few days or only made a tiny portion of the work you don't get credited in the same way than the ones who spent years on it working during all or most of the project, or at least during a long portion of time.
Hyperbole example: imagine the game has 3 music producers, 2 of them worked during the whole project or almost, across let's say 3 years. These 2 get credited in the game. The other one only worked during a couple of weeks/months doing some intern stuff and after that leaves/gets fired/doesn't pass the test period. And maybe even a big portion of what this person did was crap and someone else had to replace it or got cut. This third one doesn't get credited in the game.
There is no written rule but typically this is how it's done in the industry. Regarding the amount of work needed to appear in the game, there's no standard and even most companies doesn't have a specific amount of time working on the studio needed to be listed in the credits.
In the studio where I worked, at the start nobody got credited because the boss was afraid that the competion could hire us. Years later the bosses got credited and later everybody got credited with no specific rules. Some designer in charge of the texts of the game or some programmer simply kept updating the credits, or sometimes even the CM. In a few cases we forgot to include someone who was working during a short period of time in the game and added that person later. In other cases they weren't included on purpose. In other cases they were added as "Support artist" or "Support programmers" etc or under "Special thanks". We didn't follow any specific standard or rule, whoever filled the credits for that game decided the method.