"Does Péter have an oven?"
Translation:Péternek van sütője?
I detect a hint of sarcasm here ...but I totally take your point about the emphasis! Could you clarify the reason for the neutrality of "Péternek van sütője"? Also, how would you ask the question "Does PETER (and not someone else) have an oven?
No sarcasm at all, just trying to help. Your sentence is putting the emphasis on "sütője". So, that's what he has, not, for example, a fridge.
To have something... I think this is the most neutral order of the words, as a statement:
Péternek van (egy) sütője.
Just like in English:
Peter has an oven.
If you want to emphasize PÉTER, since the word is already in a prime location, all you can do is put more stress on it. Without changing the word order. And you are more likely to omit the word "egy".
And the same goes for a question. If you want to emphasize "Péter", you just have to put more stress on the word.
If you are asking whether he has an oven, that is, when emphasizing "van", you have more options. You can keep the word order and just say it exactly as you hear in the audio.
Péternek VAN sütője?
Or you can even move "van" to the front:
VAN Péternek sütője?
VAN sütője Péternek?
Now, back on the audio. If you listen carefully, you will notice that while she puts an emphasis on "van", she also lowers her tone (pitch?) slightly on that word, then the tone rises again toward the end of the sentence. This is when she is asking about the existence of an oven in Péter's possession.
If she wanted to emphasize "Péter", then you would not hear this slight dip in the middle of the sentence. Instead, the tone would rise straight toward the end of the sentence, without an extra emphasis in the middle, either.