So you're saying Device<-->HDMI/RJ Adapter<-->Powerline<-->House Power<--->Powerline<-->HDMI/RJ Adapter<-->Display
would not work? I don't understand why not.
Basic version
Just because two cables are the same, it doesn't mean that they necessarily are used in the same way.
The HDMI<->CAT5-adapter linked will use the same kind of cables as the Powerline, but it will use them in a completely different way.
Less basic version
The main thing to understand is that neither RJ45 nor CAT5/6 actually = Ethernet (or even network).
CAT5 and CAT6 mean nothing more than cables that conform to certain formal specifications, and RJ45 that the connector is of a certain kind. It is possible to use RJ45 and CAT5/6 in many ways. It can be used for Ethernet, it can be used for traditional phone lines, it can be used for alarm signaling, and also for raw data and other things.
The Powerline won't magically transport the signal from one RJ45 jack to the other. That would be
very complicated (read impossible) and expensive to do reliably. Now, what the Powerline device does instead, is to receive Ethernet data (and only Ethernet data) through its RJ45 jack, which it translates so that it can be sent through the power lines to another device which in turn can translate it back into Ethernet data to output on the RJ45. This way, it can route normal network connections over the power lines since they conform to Ethernet.
In case of the HDMI<->CAT5-adapter linked, it will just use two CAT5 wires to transfer data. It won't care at all about Ethernet. It uses CAT5 wiring because it is cheap, common, and pretty good for high speed transfers.
OK, maybe should have stuck with the basic version...
