Yes,
I use this to grab the access token :
curl -X POST -d "grant_type=authorization_code&code=[CODE]&client_id=[CLIENT_ID]&client_secret=[CLIENT_SECRET]" https://api.envato.com/token
I use this to output the S3 Amazon download link:
curl -H "Authorization: Bearer [Access Token]" https://api.envato.com/v3/market/buyer/download?item_id=XXXXXX
However this doesn’t truly download the files hosted on Envato’s Amazon servers:
curl -O [Amazon S3 Link with Access Keys Details]
Which outputs an empty file.
Mind you, I’m doing this from the command line but got similar results using a PHP file similar to your StackOverflow link.
Maybe Amazon has it’s own API for downloading remotely?