Not sure but I believe what you read has something to do with the diodes on the power input and not on the MIMOlite being able to invert polarity to something. If it had a a DPDT relay then it could do it but since it doesn’t I do not see how. You could remove the relay and power a DPDT relay directly but while that simplifies the circuit a bit, it may make it messier to setup. I have a MIMOlite at home that I purchased years ago for a project I never completed so I can look at it closer and do some testing if time permits (rather if kids permit).
The device you found appears to take action if a voltage threshold is reached therefore it would only help if the chicken detection sensor only had a variable analog output based on what it was detecting. Say for example that an IR barrier were enough, it could be used to force the gate open if the barrier was interrupted. Same way a garage door safety IR beam works. These barriers often have a relay in them that can be used directly without the need for the circuit you found. An example of where I did this can be seen here:
Can you share a picture of the door you automated?