The importance of a desktop PC knowing the current time could be debated, but it is clear IBM felt it to be important, for the IBM PC typically prompts the user to supply it on boot. Given that, the advantage of keeping track with a battery-backed clock is clear, and such became standard hardware from the AT on.
The importance of a game console knowing the current time is less clear, but either designers felt it so or the cost of the extra components became negligible, for consoles eventually likewise acquired battery-backed clocks.
What was the first game console to have a battery backed clock?