While everybody may use or abuse that term there is only person who popularized that term, to me, and that person does not claim to be left wing.

Trump may have popularized it, but Clinton created it [0], almost immediately after losing the election.

[0] https://www.bbc.com/news/blogs-trending-42724320

Clinton didn't create the term fake news. The article you link to mentions her having used the term in a speech, but that doesn't mean she created it, nor, as I assume we're meant to infer, that she or the Democratic Party fabricated the phenomenon referred to as a post-hoc rationalization for having lost the election.

In fact, if you read the Wikipedia article on fake news[0], you'll note the term as well as the phenomenon predate Clinton's campaign and loss, even within that campaign cycle. People were talking about it well before that point.

[0]https://en.wikipedia.org/wiki/Fake_news

The term has existed, but was popularized and brought into the common discourse immediately after the 2016 election: https://trends.google.com/trends/explore?date=all&geo=US&q=f...