Bernd, there are also songs without any singing out there
Vocals are nothing more than a bass or drums - or a guitar. They are only one part of a mix of "things" that make up a song in the end. There are no rules as to which "things" actually need to be part of a song. Ron Thal used to play "Don't Cry" all by himself on guitar at live gigs. John 5 is also a very good example of a guitarist who can pull off entire songs without any vocals - and he even released them on records!
As for this song right here, "we" are re-recording it, because a lyricist came up with a beautiful vocal line that works great with this song and the guitar line that I wrote.
Bernd, one more thing out of curiosity: You're a lyricst, so I guess that lyrics usually come first for you and then you look for someone to put music to those lyrics, right? So maybe that's why you don't feel a song is a song when there are no lyrics? Because I'm writing songs the other way round: The music always comes first. I create the chord progression, the main guitar line (or a keyboard line in some cases) - and only after that, I consider adding lyrics