There is no subway on Odaiba. There is the Rinkai line train which runs underground for some of the way. An average ride is about Y100 more expensive than the equivalent subway ride of the same length. In most cases, it is a longer walk to any destination from the Rinkai line stations than from the Yurikamome.
As to the claim that the walk to/from Shinjuku station is a problem from the Park Hyatt, the hotel runs a free shuttle to and from the station every 20 minutes from about 9 am to 9:30pm. There is another free shuttle to/from the station from the backside of the Park Tower building every 10 minutes during the day.