You can download the files by adding the lightning component on the Chatter Group Detail page, follow the below steps to add lightning components on the Chatter Group Details Page -
- Go to App Launcher and Open Salesforce Chatter.
- Click on the Group Object and select Chatter Group
- Open Chatter Group and form Setup click on Edit Page
- Drag MassFileDownloadLightningComponent on the page as per your choice then click on Save..
- Now check your Chatter Group Details Page then select the files and hit the Download Button.
- The downloaded Zip File looks like the below image
