OP, clarify the question. I have the DirecTV Genie and it is just an HDMI connection to the TV.
Yes, the box itself needs a coax connection from satt dish but, depending on your HDMI run, you don't necessarily need the box to be right next to the TV. For example, in my case, I have HDMI out to a receiver and then a long run of HDMI from the receiver to the TV (I don't recall the exact length but it's probably 12-20 feet in total). If you've managed to pre-wire for HDMI and Power for that TV, that should be good enough for the Genie. It (Genie box) will need to be around somewhere (the other end of your run of HDMI). I read your question like you are asking if you'll also need coax to the TV and that's not the case.
Another way I read the question is maybe you are actually talking about the smaller supporting boxes C31 or C41 instead of the DVR box (C34) itself. If so, they do need coax too but the answer above still applies. Put them where your run of HDMI away from the TV ends and that should work.
Maybe the problem is that where you ran the other end of that HDMI, you didn't also run some RG6? If so, RG6 is a lot easier to fish/flow through walls than HDMI.