I've found that some Stack Exchange sites quickly recommend moving a comment stream to chat after only 5 or 6 comments. But on SFF I've never actually seen this, even when comment streams have a dozen or more comments. What is the setting used by SFF?
There are two types of "threshold", and neither of them forces a comment stream to be moved to chat, only creates notifications (in two different possible places) that it might want to be moved to chat.
Users moving their own comments to chat.
When two users (just two) have a sufficiently long conversation in comments (three or four from each user back and forth in a row), the system will give an automatic notification asking the users whether they want to automatically move the comments to chat.
If this happens, by one of the two users pressing a button, then a chatroom will automatically be created, with a room name of the form "Discussion between User1 and User2", and an automatic comment will appear, attributed to the person who pressed that button, to say "Let us continue this discussion in chat" with a link to the room. The newly created room will contain all comments on the given post (question or answer) from those two users only. It doesn't work if one of the two users is suspended from chat.SE.
Apparently the threshold is: that the number of comments from each of the two users must be at least 3 on main sites, 4 on meta sites, all within a 4-hour period and with no 3rd user "interrupting". (This is information I got from an authoritative source, but it's not publicly documented anywhere yet.)
Moderators moving comments to chat.
When the comment chain on a single post, from any number of users, reaches more than 20 comments within a 3-day period, an automatic moderator flag will be raised, informing diamond moderators that the post had more than 20 comments in the last 3 days.
Any moderator can then press a button to migrate all comments on the post to chat. There is an option to simultaneously delete all comments on the post, but I personally (as a mod) usually don't do that, instead selectively deleting the least useful comments. Again a chatroom will automatically be created, but this time the room name will be of the form "Discussion on [question/answer] by User1: [title]", and all comments on the post, from any involved users (even those who are suspended from chat.SE, as long as they're still users i.e. their accounts haven't been deleted), will be copied over to the chatroom.
Both of these thresholds are the same on all sites (except for the main/meta difference). Maybe the comment chains you happen to have seen on SFF have involved more than two users whereas on other sites you've more often seen two-person conversations in comments.
The official settings are the same on every site, but there are major cultural differences between sites with regard to what kinds of comments are considered constructive and appropriate. Science Fiction & Fantasy is very lenient toward "chatty" comments on questions and answers—things that are not really aimed at improving the main posts (which is supposed to be the main reason for leaving comments). Comments on Science Fiction and Fantasy often involve tangential observations or even just jokes, which would not be appreciated on some other sites. I often leave comments on this site that I would probably delete as unhelpful natter if I saw them on the Physics Stack Exchange site (where I'm a mod).
The cultural of this site means that it is not especially common for discussions to develop in comment threads, without a strong impetus (from either the commenting users themselves or from modes) to move the threads to chat. So it's not surprising to see longer comment threads here than on other sites, where comments are policed more closely.