Why Intel 8080 CPU chip required three voltages (+5, -5, +12 V)?
Most chips from that timeframe used these three supplies (check for instance old DRAMs or EPROMs). I think you will need books or articles about details of the (IIRC NMOS) technology of that time.

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As far as I have been able to find out:

The 8080 used N-MOS FET logic, the pull-ups that are required (because there are no P-FETs to do the pulling up) were N-MOS FETs that had their gate at -5V, putting them in their linear (resistor-like) region.

The internal logic worked at 12V. This is visible in the requirements for the clock inputs: they are 0/12V, not 0/5V.

The +5V was used used for the I/O, to be compatible with the common TTL chips of that day.