It does, but, as a colloquialism, it’s reaching a disassociation from its original meaning and is now used to describe “asocial” behavior. You will often see shutins called neets (and I think this colloquial case change further disconnects the word from its original meaning) as well as someone who has a job but lives with their parents.
The word police have not been enforcing the law, so unfortunately for any pedants this change in meaning is likely to stay.
I believe that difference is down to anime fans, and the more exaggerated shut in meaning nay have bled over a bit but has not overtaken the original meaning in all contexts.
There are still many contexts where if you say NEET people will just think of the original definition, and others where people consider it the shut-in anime one.
Run-of-the-mill unemployed people that are outgoing fit the "NEET" definition better than him.
Also in Japan it seems the definition is a bit more broad than the acronym (otherwise even housewives would be NEETs): "In Japan, the classification comprises people aged between 15 and 34 who are not employed, not engaged in housework, not enrolled in school or work-related training, and not seeking work."
Self-training is definitely "work-related training". And he was doing housework.
The word police have not been enforcing the law, so unfortunately for any pedants this change in meaning is likely to stay.