If a video were to include media released under a Creative Commons share-alike license, would the final video also need to be released under a similar license since it is a derivative?
Yes. The CC BY SA is pretty clear on the topic. Per the legal text:
In addition to the conditions in Section 3(a), if You Share Adapted Material You produce, the following conditions also apply.
The Adapter’s License You apply must be a Creative Commons license with the same License Elements, this version or later, or a BY-SA Compatible License.
The way I read this is you can use the SA license or a compatible license. For the CC-BY-SA 4.0 this includes the GPL-3.0 (which would a tad weird for a video IMHO).
Now the key legal question which I cannot answer is when does my video becomes a derivative work? For instance, if I were to include to a properly attributed SA-licensed a one-minute sound clip or a picture displayed in 200 frames in a 2-hours video, would my video as a whole be subject to this license? Only a lawyer could tell.