You will not be able to communicate with the Delta 10 through a parallel port, since the control didn't have one. If your PC (either laptop or desktop) doesn't have a RS-232 port, you will have to purchase a USB to serial adapter.
The emulator software you reference on the PC is no longer supported, but for simply transferring part program files to and from the Delta 10, almost any communication software will do. The part programs are text only - there is no special formatting. I've used HyperTerminal, a communication program that is included with Windows. There are two "tricks" to using HyperTerminal: when the program asks for which modem you are using, tell it you are going "Direct to COM port," and when you go to actually transfer the file, use "Capture text file..." or "Send text file..."