From Firefly Echoes of War: Serenity Crew:
This release was first featured in Gaming in the 'Verse: Gen Con 2013 Exclusive. This title is the stand-alone version. You will need
this product, the Gen Con Exclusive, or the Firefly RPG corebook to
play Echoes of War adventures.
In theory, this is true. However, the reality of it is a bit more sketchy. Of course, with the Firefly RPG you could play- it's not out yet, however. Gaming in the 'Verse also had enough rules to play- it's just out of print. Firefly: Echoes of War includes 2 files - one is a printer friendly version of the datasheets, and the other has more background- it's basically directly excised from the Gaming in the 'Verse book. It describes what stats mean, and describes what the ship's stats mean. It however, is missing any mention of the use of said stats other than what dice to roll. There's a whole area on the intro to Cortex Plus that's in the Gaming in the 'Verse book that's not there.
What does that mean for playing? You could get another Cortex Plus book and fudge it from there- Leverage comes to mind as the only one that's actually still available on Drive Thru.
It is possible that in the adventures there could be more information on actually how to run combat and how to take damage and such- but if there's not, then you're missing some basic Cortex Plus information.