ATX 12 volt connector Z170M Extreme 4

As long as a four pin connector/cable from a PSU is connected to the 12V ATX CPU power connector on any mother board, the PC should start and be able to use the UEFI UI.

Your board's manual, while not stating that a four pin cable/connector from the PSU will work fine, does say to use the four pins on the left side, including pins 1 and 5, as you said. So we can say the four pin connection use is implied to be fine, and it is fine.

The only reason for using an eight pin connector/cable from the PSU to the board is to supply more power (Amps/Watts) to the CPU. That will be a benefit if you are over clocking your CPU, and not using any of the CPU power saving options. Using the eight pin connector also supplies more conductors and allows (in theory) more power (Watts) to be available to the CPU.

For stock CPU speeds and mild over clocks, a four pin cable/connector from the PSU is fine.

To address your question more directly, no you do NOT need to have all eight pins occupied on the mother board connector for the board to start, run, and get into the UEFI UI. You certainly can boot into Windows using a four pin ATX CPU power connection from a PSU.

There are many non-Z chipset boards that just use a four pin ATX CPU power connector on the board. An example is the B150M-ITX, which can use an i7-6700K CPU just fine. That board cannot over clock any processor because of its chipset.

It is false that you must have all eight pins occupied in order for the board to start and run the UEFI. There are many boards in use today that just have a four pin ATX CPU power connector. The fact that you are using a Skylake processor makes no difference. If a CPU required an eight pin connection, the manual would say so.

We must use at least a four pin power connection to the ATX CPU power connector, or the board and CPU will NOT start.