How to repair this cabinet door?
You would (unfortunately) have to sand and stain the whole thing.  Stain color is very dependent on a whole bunch of varied factors, and so the final color is always a bit of a guess.  In your case, you could reapply stain to the areas you indicated, since they seem to be lighter in shade.  Reapplying will darken the color and maybe get it "close enough".  Also sand back away from the stained area, but not all the way to bare wood.  Just lighten it in a gradient towards the original stained color.  Then apply your stain in a similar gradient to get it to blend.  That won't perfectly match the color, but it would fade in and hopefully be not-very-noticeable.  Exact matching, however, is near impossible unless you sand the whole thing.