Hadda Be Playin' On The Jukebox

This is my interpretation of the song:

The poem uses the analogy that the global conflicts during the cold war between the U.S. government and the old Soviet Union were gang warfare:

  "The horses head in a capitalists' bed 
   The Cuban turf 
   It rumbles in hitmen 
   And gang wars across oceans" 

The U.S. government is controlled by a few very wealthy minority and they employed the CIA as instigators and the U.S. armed forces as the muscle. The Soviet Union was also controlled by a very wealthy minority who used the KGB as instigators and the red army as the muscle:

    "Multinational capitalists 
     Strong armed squads 
 Private detective agencies for the oh so very  rich 
 And their armies and navies and their air force   

bombing planes"

There seems to be a connection between the tactics used by the mafia, and the tactics used by Government agencies to defend territory. There also seems to be collaboration between the two (mafia and U.S. Government) against the Soviet Union:

"It had to be the FBI and organized crime working together in cahoots against the commies"

The poem reaches its climax, when the result of this gang warfare between rich people is revealed to be millions of poeple killed:

   "THEY had to be rich, THEY had to be powerful 
     They had to murder in Indonesia 500000  
     They had to murder in Indochina 2000000 
     They had to murder in Czechoslovakia  
     They had to murder in Chile 
     They had to murder in Russia 

     And they had to murder in America." 

In the beginning of the poem, the author imagines and wishes that this knowledge would be distributed in every corner of the U.S:

    "It had to be flashin' like the daily double 
      It had to be playin' on TV 
      It had to be loud mouthed on the comedy hour 
      It had to be announced over loud speakers"