I wasn't involved in the kickstarter, but my understanding as someone who has been using RW for about a year and has one player out of a group of 6 who bought the player version is that the player version is meant to be a record of the realm the player has knowledge of and a place to keep game notes. It is like a diary kept between sessions.
My understanding is that the Web version will be limited in terms of how much content you can reveal for free and will not have journals (when released). Also, as others have stated, you would need Internet access take advantage of it.
At the table, players could use the player version to look up information, just as they might in a game notebook.
In my campaign, none of my at-table players have RW. I'm happy to remind them of anything that was revealed to them if they ask. I use the player view on a screen to review items I want to share with them—mostly maps.
My one player who uses RW is my one remote player. He is also the newest player, so for him it has been helpful in getting him up to speed.
I use Google Hangouts to share the player view with my remote player as well as to communicate with him during the game.
Personally, live sync is a very low priority to me. Even if all my players had the player view, it would still be low priority. Anything I want to share, I put the screen. I don't want to reveal something, say on a map, and have them all looking at their own individual devices. Having them looking together at the screen makes it a group activity. I have a player who brings a laser pointer and they can together look at and discuss maps much like their character would be.
Live sync might be more useful for remote games, but even then, I find it easier to share with Google Hangouts or some other web-meeting interface. That way I'm controlling the pace and they needn't shift their attention to another application.
Now, all this said, so many applications now offer live updates. We are so used to software like Google Apps, Office 365, web apps that save as you type, or at least when you tab to the next field, that I really would hope that someday RW way of updating and synchronizing content is modernized.
I'm hoping that the Web version will allow me to do most of the content creation and editing I need to do using modern Web technologies to allow saving as you type, etc. RW software would then, for me, be primarily a means to keep a look backup so I can use it when I don't have an Internet connection.