Nah, that’s false. Miniaturization was already underway before the Space Race. The space program absolutely benefited from it, yes. But NASA wasn’t at the forefront of those developments.
NASA literally had departments and budgets dedicated to miniaturization.
Sure, this would likely have happend anyway, but possibly later with all related knock off effects.
What are we missing because they did that though? Or what came latter? There is no way to answer this. It is easy to see what happened because of effort, but not what you didn't get (or got latter) because to focused on something else.