Your U and V values are all positive, so all quivers will point up and to the right.
I think you want U and V to be the difference between 2 and 1, and not the location of 2.
x1 = [5 5.5 6 6.5 7 7 7 6.5 6 5.5 5 5 5 ];
y1= [5 5 5 5 5 5.5 6 6 6 6 6 5.5 5];
plot (x1,y1)
hold on
x2 = [4.19 5.26 6.00 6.74 7.81 7.96 7.81 6.74 6.00 5.26 4.19 4.04 4.19];
y2 = [4.19 4.05 4.08 4.05 4.19 5.50 6.81 6.95 6.92 6.95 6.81 5.50 4.19];
plot(x2,y2)
quiver(x1, y1,x2-x1,y2-y1)
