When one creates some logical content, like in programming, only naives think that this is a rational way of thinking. In fact, this is based on patterns and intuition.
Did Wittgenstein say anything about this?
Heidegger calls this point where a logical context allows intuition to function efficiently the state of being 'expert'. It dominates most of the experience of most programmers or other craftsmen most of the time, and when it fails, there is a specific feeling of 'being thrown' out of context. (For outside touchstones, expertise is the quality of 'quality' in 'Zen and the Art of Motorcycle Maintenance' and is the mechanical aspect of Integrity (the 'Te') in some interpretations of the Tao Te Ching. It is the feeling you are most effective when not thinking.)
The context of expertise is a lot like what Wittgenstein calls a language-game, only local. The rules are unclear, but everyone has adapted to them, and this co-adaptation allows most action to be based on taste and unconscious experience.
Only the naive imagine that what goes on in the writing of prose is mostly conscious. Our grammar and rhetorical sense passes below a given level of cognitive demand when we achieve real fluency, and we enter the 'game' of writing as real players. Wittgenstein would claim that all thinking, even deep philosophical reasoning has this same character, that there are no interactive processes that do not become 'language-games' in this sense for most of the participants.
The two points of view are kind of complementary takes on the same thing. Wittgenstein was focused on how much of the game-rules we do not need to learn in order to play well, and how philosophy backs off to see the rules and tell when you are adapting them to new purposes, and when you are just outside them. He is fascinated by how much we know without knowing that we know it. Philosophy becomes a game of determining when we would be better of knowing what we do and do not know, and when we would in fact not be better off learning that.
The notion of expertise is instead focused on how much of what we could be doing consciously we would rather abandon to automatic processes, and how little we communicate about this state, and therefore most of our experience. We are experts at living, and real understanding explains that expert realm, not just the underlying pre-expert mechanical details. (The emphasis in computing is then on creating convincing phenomena that keep someone in a state of expertise most of the time without abandoning them completely when they are 'thrown'. You want things to be automatic, but not so automatic that one is thoroughly unaware of the underlying rules when one has to think through an unfamiliar situation.)