It would be much more straightforward and less tainted with perverse incentives to straight up tax the money spent by the ministries. When you set up an organization like this, it tries to expand like they all do. What Veikkaus does is try and sell people gambling products. Now government funding is partially dependent on the success of that despite it causing a lot of problems. A number of washout politicians get cushy jobs at the board and management of Veikkaus.
You can regulate private gambling companies just as well like they do in Australia.