The simple answer is yes you can buy and HDMI splitter and 25-30 foot HDMI cable and do exactly as you describe. The cables are not expensive, I just ran a 25' cable from where my Genie is located to the TV in the front overhead. The routing of the cable can be tricky but if you have the time and a bit of patience it's really not a big deal. I picked up the HDMI cable at Wal-Mart and there is no need for the over-priced under performing "Monster" cables.
As mentioned above, it still might be cheaper and easier to simply buy and install a second player but it's certainly not required.