Or rather, you're blind to everything that doesn't require a hammer.
Even in most of the examples he listed (speech/voice recognition software, translation, games, and databases), the vast majority of "code"/logic is not a neural network.
You don't "train" your UI, neural nets won't directly consume audio or spit out encoded audio, don't do HTTP, aren't an operating system and just having a game AI is pretty far from having a finished game.
Neural nets approximate and guess, but for the vast majority of problems in computing we want the exactness of code.
And coincidentally that's what makes neural networks great: They let us solve problems where stating the exact precise steps to solve them is impossible.