From the article: "But APIs are different. An API with 60 options makes for longer documentation, certainly. But if the options are well-chosen and well-documented, an API with 60 options is barely more complex than an API with 20 options. You should be able to safely forget about features you aren’t using, and just use the features that matter to you. Done well, incremental features in an API only increase complexity by O(log-n) or even O(1) – virtually no complexity increase at all."
This is true, but how is this different from a UI that's done well? With a great UI you should also "be able to safely forget about features you aren’t using, and just use the features that matter to you." Isn't that just good information architecture combined with a design that prioritizes and encourages accomplishing the most common tasks?
A poorly designed API adds just as much complexity and frustration as a poorly designed UI. But I doubt that a UI "done right" still increases complexity by O(n) or O(n-squared).