YouTube Kids will have gaming content soon, though there is no indication just yet of when the YouTube team plans to add this new content into the app. The arrival of this content for down the road was discovered in the code of the APK of the latest version of the YouTube Kids app, which will at this point be version 2.14. Although it isn't known when the gaming content will be added, it isn't hard to imagine what exactly the content might focus on. As these will be gaming videos, the contents will likely focus on games that are geared towards kids, perhaps of kids playing some of these games, similar to the wider library of "Let's Play" videos that you can find on YouTube. Although Google hasn't mentioned any announcements about the arrival of gaming content within the app, an animation icon for the gaming category is set to appear among the other options that are available in the navigation bar.
Aside from the upcoming gaming content that kids will be able to view (with their parent's permission of course), parents look to be getting a new app that caters to them. The app is called Family Link, and while there isn't much in the way of detail about Family Link when it comes to a full list of features and availability, it appears that it will interface in some ways with YouTube Kids. Family Link will be a way for parents to manage the type of content their kids will be able to watch. It's an app that can be installed on the parent's device, but also connect to the account of their kids so they can control what content is accessible.
More specifically it looks like parents will be able to block video content down to the actual video level, and block entire channels if they feel like a particular channel is something they don't want their kids being exposed to. Beyond this it also seems like parents can manage the search an content settings as opposed to just blocking specific content altogether. There's no mention of a release for this either just yet, so much of how it works and what it can do might still be in the works.