Thus, the value of the previous screen frame (t+1) is added twice, the value of the screen frame before that one (t) is subtracted, and the constant g is subtracted.
At first glance it looks like they applied a linear multi step method to estimate the value of their equation of movement. There is a huge and ever-growing number of LMM formulas and I don't think Donkey Kong placed a premium on minimizing any kind of error.
> S(0)=0 (reference position) S(1)=v₀-½g (initial velocity) S(t+2)=2S(t+1)-S(t)-g
Thus, the value of the previous screen frame (t+1) is added twice, the value of the screen frame before that one (t) is subtracted, and the constant g is subtracted.