What does by 2050 mean?

Its usually a number someone has pulled from their behind because it cannot be known.  For people who claim to know the future, they sure live poorly.

If the Tiger is gone then the villagers who must work in their habitat to survive will face one less mortal danger. And game animals will be more plentiful which will provide more protein for human beings.

It's like when your  mom tells you to be in by six. You can be in before that, but she's only going to be looking for you at 6. If you look for Bengal tigers in 2050, and they're predicted to be extinct by then, you should not expect to see any.  They might have disappeared sooner, but that's still within the truth of the prediction, since nobody can validate the prediction until the time expires.

It is an approximation. It also means if no efforts are made to stop its continued decline to extinction it will become extinct. The date given means that it is predicted that if the current rate of extinction continues by the year 2050 there will be no Bengal Tiger on Earth. That would render that tiger subspecies extinct. Extinct means gone for ever. So let us hope the prediction proves to be wrong and that steps are taken to prevent this species from becoming extinct.

It means that when 2050 is here, the prediction claims that bengals won't be any more.  Does not say when before 2050 that will happen, but says that it will happen before 2050.

The prediction part is the part that matters on how certain the result will be.  the "by time X" part just says when the prediction is pretending the event will be finished, complete.

People predict lots of stuff that never comes true.  The more certain that the predictor is about what they claim, the more likely you ought to question the prediction.  They cannot know with certainty, so if they pretend certainty, they are definitely lying.

Usually, predictions are most useful if they say "if nothing changes, then it is very likely that...".  The prediction is an extrapolation of what is actually happening, and we can say that if what is happening now keeps on happening, the result is certain.  But we cannot ever be certain that what is happening now will keep on happening forever.

They mean that when 2050 arrives, there will be no more Bengal tigers. That's the latest it will happen.

An approximation logically because they don't really know exactly for sure.