Why your current adapter won't work
Each ethernet connection has four wires. They are split into two pairs. Each pair carries one signal, one way. One pair is TX and one is RX.
The ethernet drivers may be capable of swapping the TX and RX pairs during port negotiation - on power on, and when connected to a new hub or switch. But they cannot change the TX and RX lines at other times under normal operation.
When you have two connected to your adaptors, the drivers negotiate which pair means what, and eventually the TX of one connects to the RX of the other, and the RX of one connects to the TX of the other.
Let's say you plug a third one in. Where should its TX be connected?
simulate this circuit – Schematic created using CircuitLab
Where do you want to connect the TX and RX lines of the third device? You could connect the RX to either of the top pairs, and listen in to what each computer sends, but you'd still be deaf to the other computer the RX isn't on. You could connect the TX to either of the top pairs, and send to one computer, or the other, but not both.
This coupler will work for two computers, but you need an active hub or switch that copies all the TX from every device to all the RX on every device.
Passive ethernet hubs
However, while the 10Base-T specification is specifically a star topology, and requires active powered hubs, a passive hub can be created which works. It has limitations, but it would allow you to connect three ethernet devices together:
Note that it will only work for short cable distances, and due to the voltage drop in each diode will not expand beyond 3 devices. Further it will only negotiate to 10mbps speeds, not any faster. If your ethernet devices rigorously follow the standards, they should connect to each other using this passive hub, however it wouldn't surprise me if some chipsets did not recognize this as a valid ethernet connection.
Switches are so inexpensive though, it seems odd to me that one would choose this route, but there may be specific cases where this is appropriate.
Note that TX is on pins 1 and 2, and RX on pins 3 and 6. At each device there is a transformer on each pair. Consider how this figures into the above circuit to understand how it works - or find out at this question: Building a passive ethernet hub with anti-parallel diodes .