I'm assuming the "AV cables" do not pass any other signal & are just for the alarm?
My take on it would be that the transistor switches the relay and has a resistor from base to positive power, so the relay turns on and sounds the alarm (plus possibly one of its contacts shorting the transistor so it stays in the alarm state until it is reset).
The cable socket would just connect between base and 0V, so when the chain of cables is plugged in and the far end linked to a shorted-out socket on the alarm box, the transistor is held off.
Something like that, with another resistor from "input" to +12V (something in the 1K - 10K range probably) to switch the relay on, and the external cable socket connected across input and 0V to hold the transistor off unless the cable is disconnected.
Or it could have both ends of the cable chain used, with the path through all the centre pins ort whatever as the link that shorts the input.
Use a two pole relay with one normally open connected across the transistor collector & emitter, if you do not want it to reset just by reconnecting the cables. It would only reset then if power was switched off & back on again.
(The diagram shows 12V but anything from 5V to 12V or more is OK, as long as the relay voltage is correct and suits the battery voltage range from new to exhausted. That is 1.5V per cell new down to 1V when flat, for normal cells).