Triple-quoted strings are one big string. Nothing is evaluated inside them. The % part is all part of the string. You'd need to have it operating on the actual string.
def func(animalType):
    """
    This is a sample function.
    @param animalType: "It takes one of these animal types %(ANIMAL_TYPES)s"
    """ % {'ANIMAL_TYPES': ANIMAL_TYPES}
I'm not certain this will work properly, though; docstrings are a bit magic.
 This will not work; the docstring is evaluated at compile time (as the first statement in the function, given it is a string literal—once it's got the % in it it's not just a string literal), string formatting takes place at runtime, so __doc__ will be empty:
>>> def a(): 'docstring works'
... 
>>> a.__doc__
'docstring works'
>>> def b(): "formatted docstring doesn't work %s" % ':-('
... 
>>> b.__doc__
>>> 
If you wanted to work this way, you'd need to do func.__doc__ %= {'ANIMAL_TYPES': ANIMAL_TYPES} after the function is defined. Be aware that this would then break on python -OO if you didn't check that __doc__ was defined, as -OO strips docstrings.
>>> def c(): "formatted docstring works %s"
... 
>>> c.__doc__
"formatted docstring works %s"
>>> c.__doc__ %= 'after'
>>> c.__doc__
"formatted docstring works after"
This is not the standard technique anyway; the standard technique is to reference the appropriate constant: "Takes one of the animal types in ANIMAL_TYPES", or similar.