Sometimes the spirit of a thing is more important than the letter. Even then, some official definitions show the flexibility:

http://dictionary.reference.com/browse/song — definition 2, simulating a piece to be sung: Mendelssohn’s “Songs without Words.”

http://www.yourdictionary.com/song — definitions 2 and 3, suitable for singing or sounding like singing.

Even a song with words probably doesn’t stop being a song just because one plays without singing.

Semantics and other technicalities can stand in the way of people’s involvement in music. I’ll take the involvement even if it means sometimes compromising technicalities

Very good website – however, if I may. I note that several piano websites continue to use the term “song” when referring to piano pieces. My teacher taught me that you” play a piece” and you “sing a song”. If there are no words, it is a piece.

Just a thought!!