Not at the same rates, but at higher rates than the general population and even stronger:

""" Together, our results indicate that object personification occurs commonly among autistic individuals, and perhaps more often (and later in life) than in the general population. """

This is well known for many autistic people. "I put this thing there, and now it has to stay at that position, because otherwise it will be very sad."

The surprising part is not that autistic people do have empathy for inanimate objects (this is so well known, it's even covered in some diagnostic tests), but rather to find further confirmation and compare it to the general population. Mostly because this is surprising, as in general autism is related to empathy disfunction, so it is surprising to observe empathy at higher rates (see below).

However, as many researchers have pointed out that is exactely what would be expected. Empathy disfunction is incorrectly interpreted by many as "lack of empathy". But empathy means understanding and representing the emotional state of another living creature. Assigning emotional states to inanimate objects is by definition an empathy disfunction, because you are mentally representing something that is not there in the real world. Same with over-empathy that is reported by some autistics. Since these are over-representing the emotional states of others, this is also a disfunction (i.e. a mismatch between observed subject and the representation).

So the article builds strongly on the false equivalence between empathy disfunction and lack of empathy.