Rely on you insertion of punctuation if you want but the Greek doesn't have any. I'll go with the Greek as well as other passages which I notice you conveniently ignore.
Matthew 25:46 And these shall go away into everlasting punishment: but the righteous into life eternal.
2 Thessalonians 1:9 Who shall be punished with everlasting destruction (olethros) from the presence of the Lord, and from the glory of his power;
olethros - 3639 /ólethros ("ruination") however does not imply "extinction" (annihilation). Rather it emphasizes the consequent loss that goes with the complete "undoing." [http://biblehub.com/greek/3639.htm]
Sure, it means DEATH. AS in no more life, as in no eternal life.
Strong's Concordance and Thayer's Concordance:
LSJ Gloss:
ὄλεθρος
ruin, destruction, death
Strong's:
ὄλεθρος
a prolonged form); ruin, i.e. death, punishment
Derivation: from a primary ὄλλυμι (to destroy;
KJV Usage: destruction.
Thayer:
1) ruin, destroy, death
1a) for the destruction of the flesh, said of the external ills and troubles by which the lusts of the flesh are subdued and destroyed
Ordinary usage of the word (as well as John 3:!6 as well as Malachi as well as numerous other places) say that man is burned up destroyed, that he does not have an immortal soul, that we are mortal and that the gift of God is eternal life.
To think otherwise is to believe that we don't need Jesus to have eternal life which goes completely against scripture.