19 points are how much you would get for a river that is 7 tokens long. Note that the shortest path between the tiles matter. If you have multiple rivers, your longest river matters. You created a loop of 12 water tokens, so any two of your water tokens can be treated as a start or end of the river, so you have (12*11)/2 rivers and the longest of them count. You pick any 2 water tokens on your board and the shortest path between them is one of the rivers you have. Do I make sense here?
You have a loop, so there are always 2 paths between the tiles. For example, lets consider the rightmost column of the board. You have 3 water tiles there. It would be tempting to pick the top water tile there and the bottom water tile and count all the 10 water tokens around your big tree and buildings as the path between them. But there is another path between them! Just straight up/down and it has the length of only 3. Do you see?
The river between the water tokens just above your mountains and the bottom water tile in your rightmost column has 7 tiles, no matter if you count the top path or the bottom path. For any other pair of water tokens on your board, there is a path between them that is 6 tiles long or shorter.