I just think that a strategy game such as chess can be applied to the real world and in that chess can make you a better strategical person, but how so?
Here are some example areas I think can of (definitely not limited to just these):
- Attacking your opponent at different parts of the board simultaneously. This can be translated to pressuring your real world opponent in different ways at the same time.
- Identifying weaknesses.
- A sense of danger. I don't know how well this would translate into the real world, but in chess you develop an intuition for what's really a danger and what's not.
- Calculation skills, both for thinking far ahead (depth) and considering a number of options your opponent could go for (breadth). This has obvious applications when trying to figure out what your opponent will do in politics, football, etc.
- Distributing and maximizing resources. In chess you need to figure out where to put your pieces, based on where they are most needed/can be most effective.
However, correlation doesn't necessarily imply causation. Getting good at chess might have given someone these real world skills; or, they could already have these skills and that's why they're good in both chess and certain real world activities. A likely possibility is that someone is already fairly strategical, and then playing chess amplifies their abilities.
With great difficulty. There is no real connection between chess and the real world.
What you need to apply is game theory to both chess and the other situation.
Trying to infer game theory by using chess to help your socratic method would fall way short and be much harder than doing it with math.