An author uses apostrophies on both sides of a song title rather than qoutation marks, why?

Question

It looks like this, 'Eye of the Tiger', and not "Eye of the Tiger."

Answer 1

What you call quotation marks are Speech Marks.
It signifies that someone has spoken the words.

If someone actually says Eye of the Tiger it would appear as "Eye of the Tiger".

If you are reporting that you heard someone say it, it would be written, - and then she said, 'Eye of the Tiger'.

Of course the same applies if the words are being sung.