Not at all the same.
Speaker cable is two strands of heavy wire (18-12 gauge) designed to carry a low impedance high current signal.
The TRS cable is two strands of thin wire surround by braided thin wires called the shield. It designed to carry two separate signals that are of high impedance and very low current.
I just had a look at the pdf file for your unit. I imagine that the tiny power amp in your unit is designed to work with either a 4,8 or 16 ohm standard guitar cab and that the extra capacitance introduced by the TRS cord has been accounted for and dealt with. You don't want to use a standard guitar cord (Tip/Sleeve) because that would short the left and right at the preamp. At the cab end the Ring section of the cable won't come into the equation because it only connects to the Tip and the Sleeve.
So use the right cord and rock on brother! Just make sure you put that rear switch in the correct position.
You'll probably need to make something custom, and make sure you don't connect the ring and sleeve together or you'll blow the power amp in the Engl.
I would rewire the cabinet with a jack and use a correct cable.
Yes, that product is probably exactly what you would need in your situation.