The icon just means Kentico detected a file but has no Database record of it. If you hit the import button it will create a record and generate a GUID for it.
Is the old site also Kentico? Even still there probably are references to that images which you'll break.
So you probably need to create a import for the pages and make sure all links to media is correctly mapped.
Check out the api samples for some pointers.
if you just need a way of importing all files not in Kentico yet, you'll have to create a method that reads all folders and files and tries to map it to the records in the Database.
Have a look at
CMSModules/MediaLibrary/Controls/MediaLibrary/MediaLibrary.ascx for a starting point.