@Billy That is just the textbook definition of the word. If the "song" doesn't have lyrics, the piece of music is classified as something else. I.e. there are no pieces of classical music that are defined as a song that does not have lyrics. Actually, I can't think of any that are "songs". The closest to a classical "song" would probably be an aria.
https://www.merriam-webster.com/dictionary/song@Planobilly
A bit further down the same Wikipedia article:
Through semantic widening, a broader sense of the word "song" may refer to instrumentals, such as the 20th century Songs Without Words pieces for solo piano.