In the first sentence, he is wasting time, and that is what you don't like: you don't like him [when he is] wasting time. Your second sentence is grammatical but not idiomatic. It could be said when "he is malnourished and wasting away, and I don't like those times when he is losing weight." But that isn't your intention, I am sure, to use it like "partying time" or "waiting time".
– Weather VaneFeb 14 '20 at 16:12
@WeatherVane: I disagree. Both versions are in common use today, with no difference in meaning.
– FumbleFingersFeb 14 '20 at 16:45
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Note that in some contexts, the two are not exchangeable because they mean different things. For example: I don't like him singing while his throat is sore. And I don't like his singing; it's out of tune.
– Ronald SoleFeb 14 '20 at 16:47
There's no difference in meaning. In both cases "him/his wasting time" is a clause with "him"/"his" as subject and the verb phrase "wasting time" as predicate.
– BillJFeb 14 '20 at 18:09