
The screenshot you posted shows " update " for iMovie 10 which would suggest that your Mac sees that it already has version 10 installed .
I too see the word update on my El Capitan system but this is because I have never updated to 10.1.6 from 10.1.4. I hardly use it so I haven't bothered .
When I click on update I too get the constant spinning wheel that you get , nothing else happens
I then dragged iMovie 10 to the trash BUT DID NOT EMPTY THE TRASH .
Now going to the App Store I get Install instead of update and the option to download a compatible version.
Were you the one that upgraded to El Capitan from Snow Leopard , or did somebody else do it .
Could somebody else have installed iMovie 10 ?
Do a search on your Mac for iMovie 10 to see if it is hidden somewhere .
It would appear that your Mac sees that it already has a version of iMovie 10 so try to find it .
If you do find iMovie 10 on your Mac and you want to update it, then drag it to the trash but do not empty the trash yet and see if you now get the option to install from the App Store that I got.
If you cannot find iMovie 10 on your Mac then drag iMovie 9.0.9 to the trash , do not empty trash as you will lose it for ever and see now if you get the option to install iMovie 10.
If you can install the latest compatible version of iMovie 10 then now drag version 9.0.9 from the trash before you forget, or else it will be gone the next time you empty the trash.