The tutorial explicitly configures the Nginx web server for HTTPS, has you create a server certificate and only allow TCP/443 through the firewall.
I'm not familiar with elinks' error messages so to diagnose this from the CLI you could have openssl return info with 'openssl s_client -connect owncloud.example.com:443 -showcerts' and add the certificate in say Firefox (Edit > Preferences > Advanced > Encryption > View Certificates > Add Exception) and the browse the site. If the latter works it's because the server cert is self-signed and not by one of the commercial Certificate Authorities.
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