Most Google Reader users were not using RSS before and likely would never have used them if not for Reader. They didn't kill RSS - they introduced people to it.
As someone who used a self hosted reader as well as a standalone desktop reader, the coming and going of Reader went completely unnoticed.
Ditto with browser support. Even Firefox dropped it - and they're the browser that introduced the feature! Seems silly to blame Google for the general trend.
Couldn't care less for Feedburner's attempt to monetize it. RSS is a protocol like email. Would I think positively about a service trying to monetize email?
The rest of the article is about various Google services dropping support for it.
If Google kills Gmail would we say Google killed email? It's a nonsensical thought process.
Anecdotally I found it was Twitter that killed RSS. When it was new people were using it for the same purpose I was using RSS. To follow people and organizations.