Oh, you’re right. I see now that I what I posted is mostly outside of the scope of your OP, haha. Sorry about that.
Hmm, in that case, what is it that makes you say that–or wonder if–the Japanese sentence requires a question mark? Especially since all Japanese sentences can end in a full stop. As far as I know, there isn’t a specific rule about when question marks are required, while it is a fact that a full stop is correct at all times.
If you ask me, it comes down to this.
About the English translation:
The sentence seeks confirmation from the listener. That leaves it unsure whether or not it really qualifies as a question, but the only way to convey the same message in English is by using a question. I suppose that due to the different natures of the two languages, sometimes it is unavoidable that one language uses a question while the other doesn’t.
About the interpunction:
Regardless of whether the sentence qualifies as a question, a full stop is correct. I reckon many people would use a question mark simply because it feels natural to use one with a sentence that seeks confirmation from the listener, but it isn’t required.