It is possible, but it is moderator only. We can migrate any question, anywhere. I could send this to Skeptics or Community Building Beta.
There is a bit of a complication with that, however. All SE moderators also have access to a (fairly busy) chat room, whose purpose is partially to allow us to "super ping" each other. Pinging, that is, addressing someone in a comment or chat like this:
@goldilocks, has a restriction. It only works if that user has already posted something in that context. Super pinging is a moderator tool allowing us to do that to any user from chat regardless. We can only do so in chat rooms belonging to the site where we are moderators, obviously, and in the mod chat room (more or less).
The community managers (CMs) who are actual SE staff are generally accessible there too; these are the people who, e.g., arranged our election, graduated us from beta, etc. Anyway, point being, if I did migrate this to Skeptics someone would likely want to know why in the fairly near future.
I did not investigate to confirm, but I believe the thinking around migrations has shifted over the years; right now creating actual paths that normal users can vote on via "close" is unusual but the ones that have existed (we don't have any) still exist. The number of questions that require migration is small enough to task this to moderators. I don't use it automatically; e.g. programming questions that are off-topic here are not necessarily sent straight to Stack Overflow. I have a few reasons for this:
- It is very simple to cut and paste a question anyway.
- I feel it is more polite in many cases to explain a question is off-topic and let the author decide what to do.
- Often questions would require some editing to reflect a different context.
- Sometimes this happens many hours after the question was posted, and the timestamps are not changed. This means migrating to busy sites puts such questions pages back in the "new" queue.
The question you are thinking of was deleted by the owner after I closed it here. Closed questions do not necessarily have to be deleted and some of them (e.g. most duplicates) should not be, but particularly since that one was reposted to the main site, it might as well have been.
I also wrote in a comment that the question as written was too broad and should be split up, which was why I did not simply migrate it. The OP did not do that, which was his decision to make, but got an appropriate answer that seems to have pointed him in the right direction, as he later posted a more detailed one himself. Hopefully alls well that ends well.