Is "戀"/"恋" a word by itself?
First, it is not a standard way. Apparently, it is a complain.

失~lose, 戀~love。失戀~fall out of love. The word itself has a vt+noun structure.

Try to understand it from the basic form:

為什麼我失戀了？Why I fell out of love?

One can definitely add adj to a noun(戀). (just for explanation.)

為什麼我失(全世界的)戀？

Now add adv to vt(失). (just for explanation.)

為什麼我(都失一遍)全世界的戀？

Then change order:

為什麼全世界的戀我都失一遍？ Why I fell out of each love all over the world? The singer wants to deliver a strong discourage for being a loser in love in this song.