Individuals (10 billion/1 million) do not evolve - populations evolve. Evolution takes a long time, and even the spectacularly obvious gross phenotypic changes you see between various breeds of dog, occuring over the last 10,000 years or so, has not produced any actual speciation yet. And really, unless the amount of interbreeding between two "separate" populations is infinitesimally small (or actually zero, because they are truly separate, e.g. on different sides of an impassable mountain range or sea), speciation simply doesn't happen.
I can't forsee any situation in at least the next 100,000 years which could produce two viable populations of humans which would remain separate enough for long enough for them to be considered two distinct species, and for one of them to become extinct. Evolution doesn't happen that way, or quickly enough.
I agree when looking at biological evolution, such as mutations in genes, this won't happen in 1,000 years. You're correct, the time scales are far too short for that.
In my post I was instead talking about technological evolution, though I didn't mention this explicitly, so I apologize for the confusion. The evolution of technology occurs far faster than genetic mutations, and can be more purposeful.
For example, in the near future I'd imagine some sort of intelligent A.I. will be created, running as a program, which could learn to upgrade itself by improving its source code and hardware to become even more intelligent. It'll surpass even the smartest humans shortly thereafter. Rather than waiting for a random bit to accidentally flip (e.g. genetic mutation), it'll upgrade itself deliberately to gain an advantage far quicker, shrinking evolutionary time scales down to fractions of what they once were.
I can't forsee any situation in at least the next 100,000 years which could produce two viable populations of humans which would remain separate enough for long enough for them to be considered two distinct species, and for one of them to become extinct. Evolution doesn't happen that way, or quickly enough.