Amazon CloudFront serving compressed files with Origin server running NGINX

They don't need to enable compression on CloudFront if the origin already compresses files, "if your origin returns a compressed file to CloudFront, CloudFront detects that the file is compressed based on the value of the Content-Encoding header and doesn't compress the file again." - https://docs.aws.amazon.com/AmazonCloudFront/latest/DeveloperGuide/ServingCompressedFiles.html

Note that there is a configuration for NGINX origins:

When CloudFront forwards a request to the origin server, it includes a Via header. This causes NGINX to interpret the request as proxied and, by default, NGINX disables compression for proxied requests. If your version of NGINX includes the gzip_proxied setting, change the value to any so that NGINX will return compressed content to CloudFront. For more information, see the NGINX documentation for the module ngx_http_gzip_module.