One very cool way to interface a digital controller like an arduino to a typical R/C transmitter is if the transmitter has a 'trainer' mode feature, which your listing implies it does.
What this allows is for a serial PPM data stream to be the source that gets transmitted over the air, overriding the transmitters manual stick controls and channel switches. An arduino can easily create such a serial PPM stream in software and output it via a digital output pin that could then be wired to the the 'trainer' port connector, usually on the back of the transmitter.
A second useful use of the trainer port connector is if you wished that instead of sending the stick commands and channel switch information over the air as a RF signal, there is a serial PPM datastream output pin that an arduino could read on a input pin and decode all the channel command positions, it's the reverse of the first described use of the trainer port.
Normally the trainer port is used to connect two transmitters together (usually required to be the same brand and model unless otherwise verified to be compatible), one for the 'student pilot' and one for the 'trainer pilot' and normally the students stick controls are active and his transmitter is sending RF out it's antenna, however if the trainer pilot sees trouble ahead he can flip a switch on his transmitter and the cable sends his physical control movements via a serial PPM data stream to the students transmitter that then sends that PPM stream out the RF antenna on the students transmitters, which is effectively removing all students stick and channel switch commands from doing anything. The hard part is getting the proper documentation the explains the pin connections on the trainer connector and what voltage levels the port uses and finding proper mating connectors.
I attempted to find some useful information on the 'trainer' function and how it might be useful for what your are trying to do. I won't guarantee that it's correct for this specific transmitter, but it came from drilling down in the product page:
Lefty