Hello,
This is related to the iMovie 10 update. Previous versions are not compatible with it. From what I have read, a second library would be created and a copy of the media from the original library would be converted to the iMove 10 format and placed in the new library or an empty iMove 10 library would be created so you can manually update the media later.
Are you getting an error that you cannot continue from or are you canceling after you see that error?
Update projects from earlier versions of iMovie - Apple Support
"Update projects from earlier versions of iMovie
Projects and events created in earlier versions of iMovie must be updated to work with iMovie 10. You can update when you first open iMovie 10, or you can update later.
If you choose to update, projects and events are copied into a new library that works with iMovie 10.
If the update is interrupted or takes an extended period of time, see the Apple Support article Update iMovie projects and events on a Mac."
If available it might be easier to upgrade iMovie on your old MacBook Air. After, when you first open it, a dialogue will prompt you to update the media which would create a new library that will be easier to transfer to your new MacBook Air.
"If you have not updated the iMovie app on your Mac recently, a dialog appears when you first open iMovie 10, asking if you want to update your existing projects and events.
- Click Update.
- All projects and events on any storage devices attached to your Mac are updated. You can still use the original copies of your projects and events in earlier versions of iMovie.
Important: This update dialog appears automatically when you connect storage devices that contain projects and events from older versions of iMovie. iMovie 10 creates a new library on each storage device.
If you want to update your projects and events later, click Update Later. iMovie opens an empty library containing a single event. You can use the event to quickly import media from your storage device or a connected camera, and then create a project to start editing. When you’re ready to update, follow the instructions in “Manually update projects and events,” below."
I hope this helps.