I am not really fond of Japanese pop music lyrics, but the theme of this song seems to be a boy man's anguish after being ditched by his girlfriend. In this context, what is left behind is better understood as his feeling towards her.
I agree with this interpretation.
I feel that she is not necessarily dead. She might have disappeared from him. She might get falling in love with another guy and ditched him. Of course, she might be dead of disease, accident, or suicide.
In this context, I think 愛しさ is almost equal to "love" because the theme of this song is his "lost love."
I think 置き去りの愛しさ is something like "my love that is now aiming at nowhere."
Therefore, technically speaking it means "my useless love" but it ruins the atmosphere of the lyrics of the love song.
I wonder if "my love for nothing" may work here.