I think this should accept 'He has no interest going there' ; since 'in going' and 'going' are generally equivalent.
But the "in" isn't from "in going" it's from "interest in" - He has no interest in music, He has no interest in football, etc.
Although the difference between your examples and the sentence is that 'music' and 'football' are nouns whereas 'going' is a verb. The conjunction 'in' is not there in the original Irish and to me it doesn't need to be there in the English either. To me both 'He has no interest in going there' and 'He has no interest going there' sound fine, but that is likely a dialect difference.
"in" isn't a conjunction - it's a preposition linking "interest" and the object of the interest. It doesn't matter whether the object is a verb (a gerund) or a noun - you can put any verb you like into the phrase and you still have an "interest in" doing it (or not). As for it not being in the original Irish, "aige" is in the original Irish, but "at him" doesn't appear anywhere in the Enlish - that's not how translation works.
Do any of these phrases sound better in your dialect without the preposition? He has no interest swimming He has no interest seeing He has no interest learning
OK, my grasp of grammar was always a bit ropey :-) Yes, all of your examples sound better to me without the 'in', especially if you add an object afterwards, ie 'he has no interest learning this'. South Walian English. To my ear, 'he has no interest in going' sounds long winded.
I deliberately kept the example plain (he has no interest in learning) because complicating the object (learning <something>) just distratcts from the elision of "in".
If the original sentence in Irish had been "Níl suim aige dul ann" would you have left the "in" out of "He is not interested in going there?"
And I have the exact opposite opinion. All the examples that use "in" sound correct to me, and the others sound like something a nonnative would say. We have a lot of different kinds of nonnative speakers in Southern California.
Actually, yes. It is quite common in my dialect although the other form is also used. Someone in my dialect would be strongly tempted to use the preposition I before dul if they didn't know it doesn't work in Irish