He didn’t answer the question on purpose.
Two interpretations:
Actually, the english sentence invokes interpretation #2 with me.
I’m not sure which one the finnish sentence invokes.
And I’m not sure how one would express the other meaning in finnish.
Something with “-tta”?
I agree with your interpretation, but if you look at the other translations of the English sentence, He didn't answer the question on purpose. - English example sentence - Tatoeba, it looks like they have gone for #1.
If we simplify the English we get “He didn’t do it on purpose”. Then I think interpretation #2 is obvious. What would that be in Finnish, maybe “Hän ei tehnyt sitä tarkoituksella”?
Indeed curious. My co-worker also thinks of #1. We’re both not native english speakers, so any discussion is moot.
Let’s see if some native speaker answers your question on tatoeba (or here).
Meanwhile, I learned the difference between “purposely” and “purposefully”… 
The responses I have received point to interpretation #1. Update: It has now been tagged “Ambiguous”.
I think I have found the word I was looking for: tahallaan.
The naked truth is that human language is mostly ambiguous and context dependent.
But it is utterly peculiar that “I didn’t do it on purpose” is mostly understood one way, but if you just change “do it” to “answer the question”, people understand it the other way? I find it illogical, but that’s apparently how it is. Interestingly, if you type those variants into Google translator, the translations it produces behave the same.
At least they acknowledged on tatoeba that it is ambiguous. That’s something.
Question remains what this particular finnish translation means, and how you would express the other meaning.
Wiktionary says tarkoituksella and tahallaan are synonyms, and only has one example that is not in the negative and so is obvious. That does not help.
I suspect the word order might also make a difference.
Maybe the translator made it ambiguous on purpose 