Mostly agree, and came here to say the same thing, although much would depend on proximity and context:
A pet shop employee telling a customer they've sold the dog that the customer wants: "that"
A person telling a policeman who just handed them a photo of their deceased pet asking if it was theirs: "this"
The way that Polish and English determiners work creates some unnatural English main translations. I can assure you that 'tego' is natural here, and we accept "that", but we can't make it the main answer as this would be rather confusing and inconsistent.
I believe what would make sense is English, apart from the photo scenario, would also be 'this dog that we were talking about'? Or not really?
I think this is one of those translations that you can't define exactly without understanding how the different language speakers interpret the determiners in context. I fully agree that tego is the "most correct" answer, and it maintains the ten=this, tamten=that distinction.
Interestingly, in Croatian we have three versions of the determiner: This (one here) That (one nearby) That (one over there)
Might be the first case of Polish keeping it simple ;-)