Yes, the colored circles are the connections from the LiPo monitor to the rest. The green one will be pulsing to a logical "0" when the alarm is activated.

The 4093 NAND gates in this way is like a latched on/off switch:
NAND-gate Latch
The push button ("start") at one side just need to make a short low pulse and the output to the transistor goes high and stays high.
From the green dot connection tt only has to produce a simple short pulse and the output to the transistor will go low and stay low.

The blue and black ones are the battery + and - to power the extra electronics and the 2 black open ones are parallel to the small PCB pushbutton.

So the LiPo monitor will deactivate the relay when the LiPo alarm goes off at the programmed voltage.