. . . . is the google cloud platform service required for photostory . . . .
No.
. . . . what capability or feature of photostory requires access to google cloud platform . . . .
It is the cloud import function in Photostory which used Magix Cloud Import to connect directly to Google Drive (or Microsoft One Drive) to copy media you have saved in the Cloud to the PC.
If you do not use Google Drive or One Drive, you can uninstall Magix Cloud Import