The Tango rhythm is found in many songs that we do not often think of as Tango - Tom Waits' "Little Drop of Poison" is a good example. So is "In the Deathcar" by Goran Bregovic with Iggy Pop, or "Dance with Me" by Deborah Morgan (which is actually based upon a famous tango). And "The Phantom of the Opera". If a song has that specific rhythm, then it is a Tango. And you can dance Tango to it.
But these are not Argentine Tangos. Argentine Tangos are not just songs which contain the tango rhythm - they are songs performed by, or in the style of, the great Tango orchestras of Argentina.
Can you dance Argentine Tango to other forms of tango? Of course. And it can be a lot of fun. But the dance grew and developed around the specific music, and for me at least, is most naturally satisfying when danced to that music.
Some of the so-called Neo Tango is not real Tango either - it is Disco. But if you like it, you can Tango to it.
There are also some lovely waltzes that work well - "Vals de Amalie", "Hallelujah" by Rufus Wainright", "A Thousand Years" by Christina Perri. Alternative valses are actually easier to find - anything in a fast enough waltz tempo will work.
You CAN dance Tango to these songs. But should you?
I think you should dance whatever you enjoy dancing, to whatever music you enjoy dancing it to. You can dance Lindy Hop to Rock and Roll, or Swing to Cha Cha. And you can dance Argentine Tango to any type of music you want. My husband and I will throw in an occasional Tango at a Swing Dance. But that is in the nature of a one night stand. The true, long-lasting relationship with Tango is found in the wedding between the beautiful music of Argentina and the wonderful dance that grew out of it and with it.
When I DJ I will usually include one set of Alternative Tangos - actual tangos which are not Argentine in origin. They may be Turkish, or Klezmer, or Russian, or Finnish, or American, or French, or Australian. Sometimes, depending on my mood and audience, I may include a tanda of alternative nontango music that you can dance Tango to. Make no mistake, these are not real Argentine Tangos. They are a different type of Tango experience. And that 's OK.