Sewer backup through basement floor drain after heavy rain
I realize that this response is about 3.5 years after your original post was published, but I thought I would add my knowledge/experience to possibly help the next guy.
I to live in Ohio (southwest) in a house built in 1963, and I believe I have the same set up as you.  I also just had a backup after a hard rain.
All of the following information is specific to my house, but I believe it will be applicable to you.  The pipes coming into the pit are from the foundation drainage system around the house.  The foundation drainage system directs rain water to this pit.  The drain at the bottom of the pit connects directly to the main sewer line of the house.  The main sewer line of the house is connected to the city sewer.
In a perfect world all rain water around the foundation of the house would gather in this pit, then drain to the city sewer.  This arrangement is not much different than modern setups, it just does not have a sump pump because the house is high enough to use gravity to drain to the city sewer.
In a unperfect world your house main sewer line could be partially plugged with roots (this was my problem).  When your house main sewer line is partially clogged and there is a hard rain, the discharge of the pipe simply cannot keep up with the new rain water coming in.  This is what caused my back up.    Being that the pit drain is connected to the house sewer line, that explains how organic matter makes its way into the pit during a backup (rain water and sewer using the same pipe).
At my house, I would not call the drain at the bottom of the pit a “whole house trap”.  Rather just a trap connecting foundation rain water system to the sewer line.
I have the same drain in your photo.  There is a ball in my drain.  The ball is supposed to act as a one-way check valve.  I was able to snake my drain out by pushing the ball to the side and by using a very small snake.  I should add, the ball in my drain was stuck and needed to be forcibly dislodged before I could snake.  Before I snaked my pit drain I used to have standing water as well.  After dislodging the ball and snaking, I no longer have standing water in the pit.
Hopes this helps someone understand an old house system in the future.  Thanks