In that particular tutorial, the DEPLOYMENT_KEY is simply referring to the name of the object to be stored in Amazon S3.
For objects in Amazon S3, the filename is referred to as the Key and it includes the full path, such as:
resources/aws-ffmpeg-serverless-convert/ffmpeg-1234.zip
I suspect that those lines in the MAKE file can be used as-supplied, without having to make any changes.
The $$RANDOM command will generate a random name to avoid clashes. See: Use $RANDOM in a makefile
Bottom line: You only need to change the DEPLOYMENT_BUCKET_NAME to a bucket that you created.