There are several types of empathy; I will give a vague explanation.

sympathy - yes, I know it's distinctive from empathy itself but I'm going to throw it in there anyways, because after all, sympathy is feeling contempt, sorrow and pity for someone else.. a good example in this is not performing a deadly martial art technique on your arch-enemy because you simply don't want him to go through that pain.

affective - (obviously derives from affection), in this form of empathy you will share your agony, love, grief, disappointment with (and of) other people. Clear example: everyone crying at a funeral or feeling sad for someone's deep misfortune.

cognitive - understanding motives, stressor and thoughts. e.g, you clearly understand why someone would manipulate and lie to get to the top and you fluently justify that with cognitive empathy... you know how you hear those sympathetic people vehemently moaning "I don't know why someone would kill a puppy, such a poor thing!"? well someone with cognitive empathy could understand someone killed the puppy possibly for thrill or dominance.

all have different characteristics, you see?
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Time to distinguish what forms of empathy your dad has,

most would agree that people with Asperger's lack cognitive empathy, they don't exactly understand why people do the ***** they do, it's a deficit and makes them socially inept but they most likely seem to be normal in the other 2 forms of empathy but do not exhibit it's characteristics well..

So, is your dad sufficient at cognitive empathy but sucks at the other 2?
Or is your dad sufficient at sympathy and affection but only have a minority of an issue but sucks at cognition and do you think he has alexithymia?