The definition for the word "gotten," in this case, would need to be combined with the word "over." When used together, "to get over" or "gotten over" means to overcome.
Here is another way to say the same thing: The deer have overcome their skittishness. The word "long" here implies it happened in the distant past.
You may also want to note that the plural for "deer" is also just "deer" (one deer, two deer...)!
I hope this helps!