It also depends on the context. Typing Web API everytime is stupid. We say Linux, not GNU/Linux or Chrome instead of Google Chrome.

What's the context here though?

I had to skim like 5 paragraphs to even know wtf the title meant.

In case you are asking genuinely, the "API economy" buzzword was coined a few years ago to describe business models based or largely reliant on web APIs.

The context is that it's a TechCrunch article, and I imagine much of TechCrunch's audience are not programmers and don't understand the distinction.

I know what you mean. Coming from a C background, I had the hardest time adjusting in the last few years to what "web" guys mean when they say "API".. but, language evolves, and I've come to accept it. If you can't beat 'em, join 'em.

It's just an abbreviation. They use the full "web API" in the sixth paragraph.

sarcasm?