You'd have to copy the data in C:\Users\{USERNAME}\AppData\Roaming\Garmin\VIRB Edit and transfer it the new machine, then you'd have to copy all the videos (hopefully all located in C:\{USERNAME}\schulzem\Videos\VIRB as well (to the same location on the new computer).
If your username is different, you'd have to search all the files in the first location mentioned for any occurrences of the old username and replace it with the new one.
The good news is that we are working on a feature that will make this a lot easier, the bad news is that I cannot promise this will be done very soon.
In regards to a feature or tool you mention (and also some mention here relating to moving database), would this also allow you to switch back and forth between PCs/devices?
e.g. I use VIRB Edit on my desktop in the main, but if I'm on holiday or trip away I may have my Windows tablet with me, and while it's not as powerful it's able to do modest edits I can publish at the time. However once done I'd like to be able to sync the video to the desktop so I can continue or re-edit on the desktop, complete with synced/adjusted G-Metrix data. I'd continued to use both the tablet and desktop for VIRB Edit though, not just migrating from one to another and only then using the new instance. Though I don't mine the videos being removed from the tablet once done, but I also don't want to lose existing videos on the desktop.
I think we'll target a simple migration mechanism at first. Syncing different machines would be nice, but will probably not be in the initial implementation.