How to read the circuit to drive the numerical value of Vgs1?
When doing DC analysis (large signal analysis), you remove all AC sources. That means replacing AC voltage sources with shorts. (AC current sources would be open. It is like replacing the source with its ideal internal resistance)
So in the DC model transistor's gate is connected through Rs to the ground. There is no current flowing to the gate, so the voltage drop across Rs is zero. That means the voltage at the gate is 0V (ground). Vss is -1.25V. Vgs is the difference between the voltage at the gate and Vss, which indeed is 0-1.25=1.25V.