Why are enynes named as -en-yne and not -yn-ene?
The current version of Nomenclature of Organic Chemistry – IUPAC Recommendations and Preferred Names 2013 (Blue Book) reads as follows:


  P-31.1.1.1 The presence of one or more double or triple bonds in an otherwise saturated parent hydride (…) is denoted by changing the ending ‘ane’ of the name of a saturated parent hydride to ‘ene’ or ‘yne’. Locants as low as possible are given to multiple bonds as a set, even though this may at times give ‘yne’ endings lower locants than ‘ene’ endings. If a choice remains, preference for low locants is given to the double bonds. In names, the ending ‘ene’ always precedes ‘yne’, with elision of the final letter ‘e’ in ‘ene’. Only the lower locant for a multiple bond is cited, except when the numerical difference between the two locants is greater than one, in which case the higher locant is enclosed in parentheses.
  (…)


Since, in names, the ending ‘ene’ always precedes ‘yne’ (with elision of the final letter ‘e’ in ‘ene’), the given compound is a ‘hept-x-en-y-yne’.

Since the lowest sets of locants in ‘hept-1-en-6-yne’ and ‘hept-6-en-1-yne’ are equivalent (1, 6), preference for low locants is given to the double bond. Therefore, locant 1 is assigned to the double bond and locant 6 is assigned to the triple bond.

Thus, the correct name is hept-1-en-6-yne.