I think it's still surprising, if not "paradoxical" (obviously it's not paradoxical if it's reality).

The difference is: in your two examples we know there's a delay, and all you did was say that some people will know the result before others who are receiving the delayed result.

What the original question is saying is that you can't ask "well, what is happening right now on Proxima Centauri?" since the very question of "now" is not specific. I think that's quite different.

On Earth, with Newtonian physics, we intuitively think that "now" is shared, so we really can say "I wonder whether someone has scored a goal now," and the answer shouldn't depend on whether you're in a car or not.