Every time the 4017 is triggered by the 555 it switches on one of ten output pins in order. Then it goes back to output pin one (actualy the output pins are 3, 2, 4, 7, 10, 1, 5, 6, in sequence from 1-8).
These pins have to be separated (not connected) which I think is wrong with your circuit).
Your circuit uses only pins 2, 4, 7, 10.
This implies there are only 4 different sequences in turning the stepper motor. Coils A and B are switched on simultaneously (presumably by pins 2 and 4. Then coils C and D are powered, presumably by pins 7 and 10.
Perhaps the circuit could be fixed by removing the conductor connecting pins B and C (ie the connector from pin 4 to the 4.7K resistor leading to coil C.
If you were trying out this circuit, you would get your stepper motor and 4017 connected up and trigger the 4017 by applying a positive voltage to pin 14 (the trigger) and seeing if the stepper turns.
The TIP's are darlington pair transistors increasing the output power of the 4017.