Perhaps this is getting unfairly downvoted because it isn't a question about a concept or argument.
I imagine that the most popular games with rationalists would be puzzle games. Here are a few that are considered the greatest of all time:
These are interesting games because they involve intricate reasoning, thinking about sequences of dependent actions, and inference in the presence of partial information.
I'm curious about your saying you can't "simulate" visual thinking since visual thinking is remembering a diagram or spatial representation of something and reasoning about things on this mental map.
So, can you imagine a picture of a sailboat? Now, someone uses a visual analogy and suggests that the economy, your life goals, your relationship is like a sailboat. As soon as they start talking about, say, the business climate being the water, wouldn't you start to think ahead (from your mental picture) about what the "wind" would be, how you would tack your "sail" (and what that sail might be) in order to move the "boat" toward your goal?
Your mental model guides your reasoning by letting you use intuition and judgement about the imagined scene. The visual layout helps partition the problem into the interrelated parts, their relationships and mechanisms of interaction.
My example may not be the best one since the difference between a plain-old analogy and a visual analogy is probably that in a really rich example of visual thinking, the spatial relationships, shapes and connections between them are much more essential and informative than my sailboat example. They help you reason about causes and effects and theorize about consequences of imagined changes in a concrete and useful way.