I cannot say with certainty, but when I read it I believed it referred to those of us who are currently alive. Events 250 million years from now are well beyond the period we might likely live to, and beyond the period anyone we meet might live to, and so Cecil makes a bit of fun by suggesting that means we don’t care.
Of course, all of humanity might be dead by then too, but that too wouldn’t really matter to us. Or humanity might be so changed by then that we would not recognize it as being the same species. Again, being long dead we would be affected by this very little, if at all.
There is a pretty small window of history that really matters to most of us: if something happened so long ago that you’ve never met anyone who witnessed it, it isn’t really personal to you, and if it will happen far enough in the future that no one you’ll ever meet will see it, again it doesn’t really matter.
We all know that the planet is ultimately doomed, that the sun will eventually go cold or explode, but that won’t happen to our children, or grandchildren, or even great-grandchildren, so it doesn’t really seem real.