Frankly, the question you've linked isn't physics at all. You're just asking
How can [mathematical tool] be applied to quantitative finance such as option value calculation?
and that is purely a quantitative-finance question; as such it belongs on the Quantitative Finance Stack Exchange site (which opened to public beta in February 2011).
I really don't see how "but [mathematical tool] was developed for use in physics!" is a relevant argument. The same is true for calculus - does that mean that all questions about differentiation and integration are on-topic here?
It's pretty telling that the supporting argument for this,
much like how engineering physics is physics with engineering application bent,
goes a good bit of the way towards sinking the general argument: generally speaking, engineering questions are not considered on-topic here. While it uses concepts from physics, engineering is a separate discipline and to really do engineering, one needs to know and apply a whole host of separate tools, concepts and frameworks, which have nothing to do with physics. So, if the question is "which laws of physics underlie this engineering solution", that's a physics question, but if it's "how does one use X physics to solve this engineering problem", that's an engineering problem. The question linked here falls strictly on the not-physics side of the divide. Heck, if it were asking "how does one link the uses of path integrals in physics with those in finance?" you could argue that it's a multidisciplinary question, but that's not how it's been phrased.
As for this,
Not to mention closing a question when the answerer hadn't even done with his answeris plain-- how to put it nicely-- rude
the presence or absence of answers, let alone whether the answerer has further edits planned for that answer, is irrelevant to whether the question is on-topic. Closing questions is supposed to prevent answers, so the correct reading of "I was writing an answer but the question got closed" is "I chose an off-topic question to answer".
In any case, though, from the understanding of the site's scope as it has matured in the years since this question was posted:
Should we allow econophysics questions?
So long as they have a nontrivial component that's directly asking about parts of physics, then yes. If they're asking how tools from physics can be applied within other fields, then no.