How is this relay circuit Working
The MVT600, whatever it is, it should have the ground connection, without which it can't possibly control the relay solenoid. 

Having said this, the function of this immobilizer is easy to explain. MVT600 normally keep the relay switched on thru pin 85 and 86 by pulling the yellow wire to the ground. This in turn closes the relay contacts (pin 30 and 87a) so that ignition key is enabled. 

When the immobilizer is active, the yellow wire is left floating and relay is killed thus cutting off the 12V to the ignition key.