This all began in the 1970's when National Semiconductor brought out a series of integrated circuits for alarm clocks, clock radios, clocks for cars and so on. These chips included the LED display driver and the timing clock usually came from the mains.

Here is an example with the page of the data sheet regarding how the snooze function works:

http://html.alldatasheet.com/html-pdf/9252/NSC/MM5387AA/168/...

When the alarm goes there is a 'latch' that is operational for 59 minutes. Pressing snooze does not turn this 'latch' off, it suppresses the alarm output for 8-9 minutes. Turning the alarm off is what resets the 'latch'.

Chips of this era worked on BCD - BCD ruled once upon a time, when people did things in FORTRAN...

I don't think that National Semiconductor deliberately sought to emulate the snooze time of analog alarms from a previous era, it just was do-able to do 8-9 minutes in available silicon.