There are classical pieces called "vocalese" that have no words - just a syllable. Rachmaninov wrote a bunch of those as did other classical composers. They are "songs." Jazz singers do the same thing, kinda. They take instrumental jazz standards and sing and scat to them.
As for pop songs, "Walk don't run" by the Ventures is a song though it doesn't have any lyrics. The melody is "sung" by the guitar.
This is my opinion on what makes a song today: If it has a good melody (that could be very subjective) either by instrument or voice being used like an instrument even without words then it is a song. Something you can sing/hum. If it just has a bunch of riffs, than it could be categorized as something else - like some "dance" tunes or noise/experimental bands that create soundscapes.
This is a little off topic, but I guess keeping in mind that
originally, the voice was the first instrument. All other instruments after came as a way of imitation of the voice. 1-2 thousand years ago, when most Western musical instruments were being developed, the voice was the highest form of music. (please don't go into a religious debate here, this is just for historical purposes) Music history directly correlates with Church history. The Catholic Church still holds the voice (chant) as the primary means of worship and then the organ. All other instruments are to be used as exceptions (this is even supposed to be true for today). Going back, Church music is a direct descendant of Jewish worship music, so this tradition of Western religious music holding the voice as the primary means of song has a deep history.
People could argue that drums are not imitating the voice, but drums are less of an musical instrument in Africa and more of a means of communication in their
original context (and still used that way now). The drum beat could be heard from great distances to communicate - like using moris code. Does that mean that African drum ensemble performances are "songs?" Not by some definitions; but maybe because it is communicating, it could be.
It probably just comes down to how one categorizes "song" and its sub-genres. Or "song" is a sub-genre. Or all songs are music, but not all music is song. Or "all squares are rhombi but not all...." Or all mammals have bellybuttons, except the platypus which was given a duck bill, venom and electolocation to make up for being hatched. You lucky Australians.