https://en.wikipedia.org/wiki/Button,_Button_(The_Twilight_Zone)

Yes, that somewhere in the world, someone she doesnt know will die.

When Mr. Steward returns to collect the button box after the button is pressed, the lady asks what happens to the box next. She is told it will go to someone else with the same offer, with assurances that the new recipient will not know who she is. As the previous commenter said, the wording deeply implies she would be the certain "someone" targeted by the next button press.