For most of the metrics you’ve listed, you can get that by polling the Get Streams endpoint https://dev.twitch.tv/docs/api/reference#get-streams or for followers the Get Users Follows endpoint https://dev.twitch.tv/docs/api/reference#get-users-follows
That’ll give you the number of current viewers for each stream. For average, peak, time watched, etc… you’ll have to calculate that yourself.
As for data on games, you can use that same Get Streams endpoint and specify the game ID to get streams for just that game. So to get number of streams you would get streams for the game, paginate a few pages and see how many streams there are. For minutes watched you would do the same but sum the viewer count for all those streams etc… it’s all metrics you will have to calculate yourself.
Some things, such as game engagement, game followers, and page views, are not available through the API.
It is also worth noting that there will be a margin of error for game analytics, as to get things like number of streams (and from that, viewership) the Get Streams endpoint by design has progressively larger error rates the further you page through it. If you want accurate data you need to use the Insights provided to Game Developers.