Introduction to IP : Laplacian of Gaussian?
You are right about the $x$ and $y$ values. The center of the matrix is $(0,0)$ and the corner points are $(\pm 4,\pm 4)$. But they obviously wanted integer values in the matrix, so they simply scaled the LoG function by a factor of $482.75$ (just to get a decent range). Evaluating the function with this scale factor gives you (for the lower right quarter of the total matrix):


LoG =

  -40.000000  -23.086993    0.294243    5.218347    2.080704
  -23.086993  -11.762411    3.077873    4.839310    1.745668
    0.294243    3.077873    5.409023    3.361998    0.998325
    5.218347    4.839310    3.361998    1.456020    0.365518
    2.080704    1.745668    0.998325    0.365518    0.081641


Rounding should give you the final result. However, if you look closely, you'll see that it doesn't (at least not for all $(x,y)$ values). If you check the matrix on this page, you'll see that for the same $\sigma$ it is also different. So people make mistakes and they just copy from each other.