Those video inputs are composite which is analog standard def. The source from the box may be digital but it will be analog standard def composite at the TV.I agree.
But I think the digital TV operation definitely works here using the IR remote repeater technology that you can see on the picture on the link. The digital set-top box is controlled remotely via the IR repeater and the Transmitter takes inputs from AV outputs of the set-top box. This is my assumption.
There are transmitter/receivers that do transmit an HD signal but they are also not cheap.
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