Great ideas!
I really like the "Boss battles for higher levels of learning". It conveys the amount of work and perseverance that is required in order to learn.
It is possible to develop something like StarCraft or League Legends for forecasters but perhaps the game goals will be a bit removed from immediate meteorological knowledge. Forecasters could review weather data and decide where to deploy a team of observers to provide early warning. If the team is in the wrong place, there will little warning and infrastructure will be damaged.
Tsvet