Is 360 video editing the same as traditional video editing?
Usually 360° videos became 360° only in realtime during playback. You can see it:


Go to to this video (youtube now supports 360° videos)
Now, using Chrome install this extension (it will disable HTML5 player)
Try to see video from the point one again.


You will see something like that:


That happens because Flash player don't know how to interpret 360° video and showing original state of it.

So, during editing your 360° video can be displayed as normal video with huge distortion. If you can handle that, than you can edit it in any program of your chose. 

Good luck!