By default, SME attempts to deliver email directly to the recipient's SMTP server - so your server-only system is trying to deliver email all over the Internet...
By default, SME has an "SMTP Proxy" enabled in server-gateway mode to intercept all outbound smtp traffic and relay it. I'm not sure what is required to make this work; I always turn it off...
So, you'll probably get behavior closer to what you're expecting if you disable the SMTP proxy on the server-gateway system at server-manager:Security:Proxy settings