The HR34 Genie has an ethernet port. You can plug in your router there and it will work.
However the HR34 can connect to the internet via the coax connection. So what DirecTV does is put a BB DECA or CCK to the coax and connects it to your router. This is the only connection they officially support.
These are free from DirecTV for new installs. Not sure if they charge you for it afterwards.