You've omitted the word "primarily" in your quote, and it was an important one. But let's take a British tabloid like the Daily Mail. The Daily Mail has a distinct agenda, but the _primary_ purpose of content in the Daily Mail is to sell copies of the Daily Mail. The Economist has an unrelenting neo-liberal agenda, but again the primary purpose of content in The Economist is to sell copies of The Economist. These publications are rarely considered to be propaganda.

Some commercial or semi-commercial publications explicitly have aims of propaganda. The Guardian was founded to explicitly push an agenda, for example. Generally one tends to refer to this as "media bias" or "editorial slant" to distinguish it from propaganda pushed by governments.

This doesn't necessarily imply that all state-owned or non-commercial news outlets are propaganda, although I think one's starting assumption should be that they are. The BBC's World Service definitely serves (served?) the British Government's aims abroad, and was explicitly funded as such. _However_, good-faith accusations of it publishing propaganda are pretty rare, presumably because it's considered more useful by the UK to be a publisher of news that people will believe, rather than pushing a specific angle.