I challenge you to provide a sound definitionI'm certainly not up to that task. But I think that lay people are using the term more generally than you are. The Wiki you cite has multiple, expanded, definitions in the section titled "other uses of the term". For example:
One common practice of high-frequency traders
(HFT) is a form of front running, where they
peer into various exchanges and try to detect
orders as they propagate from a broker's order
router.
That's not front running by its traditional definition. But that's probably one way that Virtu makes money.
The English language (or is it the American language?) is not static. Words change meaning all the time. E.g. take the word "gay". Once it meant happy, then it became a pejorative, and most recently it has been embraced by the LGBT community. That word sure has changed meanings over the years. Rather, it probably has retained all of those meanings. https://en.wikipedia.org/wiki/Gay
Edit: forgot to add this:
I would suggest that simply processing and executing orders quickly on the basis of public information is not sufficient.
Here's an example of using what should be non-public information. Various exchanges, who investors reasonably thought were working on behalf of investors, in the public interest, were instead working for HFTs (from whom they made the most money). Hence "flash" orders, where an exchange would take an order it received from the public and "flash" or show it to its HFT buddies.[1] I don't know if the SEC finally banned that.
How did receipt of my order at an exchange turn into "public" information ahead of its execution?
[1] http://www.wsj.com/articles/SB124940289965505053