I know that millenium has other meanings, but how does that fit in with the father's response, which seemed to indicate the millenium is a particular date?
Also, I don't see how any of those other meanings combine with "space atrophy" to make "heat death of the universe".
I agree it's possible this is a new idiom invented by that society, but in that case, I think it was a confusing thing to do, given that the rest of the piece was very contemporary and normal in its language.
Certainly, the point is that the narrator is going to live a very, very long time. As far as that goes, I think the story is perfectly clear. And that is really enough for it to work. But I think the actual phrase was confusing and, if indeed it is one of the more poetic uses of the word, somewhat out of tune with the rest of the story (which is just a nitpick, I should add, and I don't mean this as substantive criticism).