Hi there, I'm an engineer who works at [INSERT FANG] creating models of user behavior and systems that use those models to drive [INSERT METRIC].
The key here is to further define "a sufficiently high degree of accuracy." Sufficiently high degree of accuracy to... do what? Predictions from these models are typically only sufficient to move [INSERT METRIC] in the aggregate, there is no need to be more accurate than that.
For your case: most of these models are noisy and operate over sparse data. That means any individual prediction can be arbitrarily bad, even to the point of complete randomness. The models only need to be marginally more accurate in aggregate than the a priori average prediction for each item without conditioning on any user features.
Your intuition is correct. "Computer algorithms ... can now infer ... your moods, your political beliefs, your sexual orientation and your health" in the context of this article is hyperbole.
For instance, to predict moods you need to source ground truth variables. Users don't normally give this information out for free. Even in the case the user updated their status with "My current mood is x" there is bias you have to account for that is likely prohibitive to the task. People self censor their emotions on the internet. This means sourcing the data in some other way, maybe through a questionnaire. Either way you won't have nearly as much data and the resulting model will likely be much noisier. Modeling the other user features mentioned have similar pitfalls.