I think in this case, a "dramatic interlude" (lower case) refers to an interlude that is of a dramatic nature. In other words, the players have a filler event of the GM's creation that is exciting.
However, there are two published variations that were released after Slipstream, which used similar wording. Feel free to use either of them in your Slipstream campaign if you don't want to create something on your own.
Dramatic Interludes (web supplement)
In 2009, Pinnacle released a free web supplement called "Dramatic Interludes" (upper case). Unfortunately, Pinnacle no longer hosts this on their website.
The idea for this was that instead of saying "you travel for many days and nights to reach your destination", you draw a card and determine what event happened to your character along the way based on the number (along with a mechanical advantage or disadvantage that will carry over). Players then elaborate on this event with a short story, with most results encouraging players to incorporate part of your character's backstory into it. For instance, if you draw a 7 or 8, the outcome was this:
7-8 Trial: A part of the trip was particularly grueling, exhausting, or mentally draining for your hero. Suffer a Fatigue level for the next 24 hours and describe what happened. Work in an anecdote from your past into the tale.
Interludes (Savage Worlds Deluxe and web supplement)
A simplified version of this system, called "Interludes" was included in Savage Worlds Deluxe. If you don't have this in your book, fear not because Pinnacle released a free web supplement containing these rules for those who had earlier editions.
In this version, the goal is to replicate downtime, such as sitting around a campfire or talking along the way of a journey. Players draw a card and are asked to recollect a tale from their backstory based on the suit. For instance, Clubs is the following:
Clubs—Tragedy: Describe a tale of tragedy or misfortune from your hero’s past, featuring one of his Hindrances if possible. If the teller has a dark secret of some kind, hint strongly at it, drop clues, or otherwise give the rest of the group a glimpse into your hero’s dark side during your narrative.
Choosing to tell a tale awards the player a Benny or Adventure Card, but otherwise has no mechanical effect.