It is saying the Edge (...Microsoft.MicrosoftEdge_41 ...) needs to be closed for the update to work.
So shut down all Edge sessions, the go into the store and try to apply the update to Edge.
EDGE
WHAT TO DO IF MICROSOFT EDGE ISN'T WORKING
https://support.microsoft.com/en-us/help/402356...
Here are some common solutions to problems with Microsoft Edge. If you can't open Microsoft Edge, or if it opens briefly and then closes, try the following:
REINSTALL EDGE:
http://www.intowindows.com/how-to-reinstall-mic...
BEFORE resetting Edge, you can back up your Edge Favorites from the Settings pane or using the Manage Edge tool, http://www.emmet-gray.com/Articles/EdgeManage.html , which also gives more flexibility for managing, ie Export to HTML, or moving them
HOW TO BACKUP AND RESTORE MICROSOFT EDGE FAVORITES IN WINDOWS 10
https://www.tenforums.com/tutorials/7256-backup...
• Option One: To Import or Export Microsoft Edge Favorites as HTML File
• Option Two: To Backup Favorites from Microsoft Edge
• Option Three: To Restore Favorites in Microsoft Edge
MANAGE, RESET AND RE-INSTALL EDGE
http://www.emmet-gray.com/Articles/EdgeManage.html
https://www.groovypost.com/howto/reset-microsof...
WIN- Reinstall Microsoft Edge
Open Start menu,
type: powershell
Right click powershell
click on “Run as administrator”
At command prompt, type:
remove-appxpackage –name Microsoft.microsoftEdge –Verbose
Get-AppXPackage -Name Microsoft.MicrosoftEdge | Foreach {Add-AppxPackage -DisableDevelopmentMode -Register “$($_.InstallLocation)\AppXManifest.xml” -Verbose}
Exit PowerShell, restart, then try again.