How these two diodes used in the ciruit protect from the voltage spikes?
If the IO is sequenced correctly, that protection scheme should work.  Basically if the "inactive" pin is held at ground, and the "active" pin is pulsed high and then either released to high impedance or just pulsed high-low, the coil is going to try to pull the "active" pin below ground -- and the Schottkey diode will do it's job.

Since it's a DIY project, you can always change the protection scheme to please yourself.  I'd probably use a simplified version of the DigiKey schematic, with the Schottkey pair at the micro pin, then a series resistor to the coil.  If you really want to be paranoid, use four transistors off board of the micro and drive them with four pins, scheduled to make a nice H bridge.