Your are correct, we didn't account for the additional gravity from the sugar, but that would be less than 0.5% abv. Depending on how much priming sugar you add, you will add somewhere between .002 to .003 to the gravity (equivalent to .25 to .4%abv), but....... you are also adding additional water which will dilute that increase some. ........ Correct; it does slightly increase the final alcohol.
Where does the 131 come from?
Alcohol by weight = gravity difference x 105
Alcohol by volume = abw x 1.25
I'm sure both of those calculations have some rounding to them. The 131 comes from the product of 105 X 1.25.
For most of us, multiplying by 131 is simple and easy to remember, and is close enough.