NOTE the sentence: "we can be confident that “the Judge of all the earth” will do what is right"
Jehovah JUDGES those at Big A and if those that are not baptised but are deemed to want to turn to JW have a chance to be saved but no-one can say for definite who.
NOTE the context of the phrase "But a person’s eternal future does not depend on when he happens to die."? What precedes it is: "It would almost be better if my relative dies before the great tribulation begins so that there is hope for his resurrection.” There are surely kind motives behind such expressions."
The context of the phrase about "a person’s eternal future does not depend on when he happens to die" is about those wanting family members to die before the Big A (or those not heard their preaching work).
NOW note the sentence on Jehovah being a judge...which occurs at the Big A!
How on earth can you think when they say "But a person’s eternal future does not depend on when he happens to die." means EVERY person gets through the Big A without being judged is utterly preposterous.
The article clearly says there is a judging...it is just they are not so dogmatic in that it will be JUST JW's that get through. Rather they are saying JW's and some non JWs who have a good heart or those who have a good heart who haven't heard the good news may get through.
AND therefore JW dubs shouldn't wish that their family die before the Big A as Jehoover may still get them through IF they are judged worthy.
It really isn't that hard to understand.
Note the next paragraph:
Through our study of the Bible, we have come to know just how much Jehovah values human life. He gave his Son’s life so that all of us may have the prospect of living forever. (John 3:16) We have all felt Jehovah’s tender affection. (Isa. 49:15) He knows each of us by name. In fact, he knows us so well as individuals that should we die, he can re-create every unique detail and restore every memory that makes us who we are! (Matt. 10:29-31) Surely, we have good reason to be confident that our loving heavenly Father will judge each individual in a perfectly balanced, righteous, and merciful way.—Jas. 2:13.
There is a still a judging of every person at the Big A and nothing has changed there! Most will perish according to their current doctrine, it is now just some not JW's get through based on Jehovah the perfect judge etc.
The whole three paragraphs are trying to help JW dubs NOT wish their unbelieving family dead (or those not ever heard the preaching) now so they get through the Big A as the only previous way to get into paradise if not a JW was to die prior to the Big A.
Now they don't and simply rely on Jehoover the judge and they are simply softening their previous very dogmatic stance.