I guess it just means "even though this machine looks like a desktop computer (which it very much usually was as a NeXT station), it's actually acting as a serv

I guess it just means "even though this machine looks like a desktop computer (which it very much usually was as a NeXT station), it's actually acting as a server, so please don't shut it down like you would with a desktop machine". It by far wasn't the only "server" at that time. The WWW may be 30 years old, but the Internet is much older.