You have to pay for an additional multiroom subscription if you are an existing Sky subscriber, so no, not free to you! EDIT: Seems it may be different if you are unfortunate enough to have Sky Broadband.
Where does it say I need multi room?
Per the Sky/360 website said:
To watch Sky Player on your Xbox 360 you need an Xbox LIVE Gold membership. Live TV channels depend on your subscription. Price and availability of on-demand content depends on whether you are a Sky TV/Sky Player TV customer and the kind of subscription you have. Some programmes from live Sky TV channels are unavailable to show online (see sky.com/skyplayer). Your subscription will renew automatically unless you tell us otherwise. Minimum 2Mb broadband connection recommended. PC with Microsoft Windows XP or Vista or Intel based Mac required for Sky Player on your computer. Information only applies to residential customers in the UK, ROI, Channel Islands and Isle of Man. Further terms apply.