Endgame is a term from chess that has made its way into wider usage, so I think it is not precisely a coincidence, but both taking it from the primary source.
from <a target="_blank" href=http://www.dictionary.com>www.dictionary.com</a> :
end·game also end game Pronunciation Key (ndgm)
n.
1. Games. The final stage of a chess game after most of the pieces have been removed from the board.
2. The final stage of an extended process or course of events: the diplomatic endgame that led to the treaty.
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