Your fritzing did not make it. This ESP8266 Beginner's guide may be of interest.The L293 logic supply voltage is 4.5 minimum. So you will need a 5V supply for it as well as 3.3V for the ESP and level shifters on the ESP inputs. Also they are ancient and inefficient technology (crap). Polulu has a wide range of motor drivers that will work at 3.3V logic levels.
These do not require any driver?
Yes, all motors will need a driver to work with a ESP8266. The ESP8266 only outputs 10mA (max recommended), far to little to drive a motor. The link to Pololu DC motor drivers in reply #1 has a selection of drivers. To choose a driver, you need to know the motor supply voltage and the stall (starting) current. The stall current should be listed on the motor's data sheet. If not it can be estimated by measuring the motor coil resistance and dividing the supply voltage by the measured resistance.
I did not know that stepper motor requires constant power to keep still,