Calling instrumental pieces "songs" does exist in real-life common usage even if it's not "technically" correct. After all, the ancestor post did just that.
Depends how prescriptive you want to be.
A classical music lecture series I listened to [1] claimed this came about because that's what iTunes calls all tracks/pieces/songs. Seems plausible, but probably other MP3 players did the same thing too.
[1] Sorry, no link, don't remember what exactly it was.
Felix Mendelssohn wrote a collection of pieces called Songs without Words for the piano. This might suggest that the term "song" can be more nuanced than simply whether or not there are vocals.
The original German title is "Lieder ohne Worte" (https://en.wikipedia.org/wiki/Songs_Without_Words), and there is AFAIK no strict requirement for lyrics to count as a "Lied" (or at least "Lied" is not connected to "singen" the way "song" is connected to "sing").
No no no, the second letter functions like a power button. i means on, and o means off. "Song" means the vocals are off.