A few things:

• Many (most?) ratings these days are self-assessed by the developer/publisher.
• The review process has been heavily streamlined through IARC, so you can effectively get ESRB/PEGI/etc simultaneously. Governmental ratings (like GRAC in South Korea) still require you go through the government agency – but some stores like Epic or Oculus can effectively do this for you – and even then it’s still self-assessed.
• Some of the storefronts offer help with ratings, in a way doing what a publisher would do, if you self-publish. You take a quiz to determine ratings and ask questions before the rating boards even know you exist.
• Ratings boards don’t typically play the game. Sample screenshots and descriptions can be included in some submissions, especially if there’s a grey area or the submitter is inexperienced, but it’s often just apply and get your cert.