I suppose one way it might end up handy is for out-of-game guild communication. "@RaidLeader - Not going to be able to make Ulduar tonight. Family aggro.", "@GM - I'm gonna be on one of my out-of-guild alts if you need me.", "@RandomGuildie - Yo dude, get online. Throwing together a Naxx run" etc.

I know a lot of guilds have forums and stuff set up for that, but this might prove to be faster/more efficient. Beats logging into the game to send an ingame mail certainly.

Thinking about it more, I'll have to keep an eye on the service. Would be handy if they implemented features like that.

Well as you say, there's plenty of guild hosting services out there that provide forums and additional features such as raid scheduling.
The main difference between Twitter and other online communication is not speed or efficiency but that it is meant to be an open, public speaking place where you can listen to people without an invite or password. That conveys certain advantages for celebrities, micro-bloggers and anyone with another web service that they want to promote - where they want the readership to be as wide as possible. Twitter fans also claims "news" spreads faster on their network than on private networks as they are more "connected", which is debatable.
Anyway, I can't honestly see any of these advantages pertaining to WoW. It just looks like some enterprising individuals are just hoping to jump on the Twitter publicity bandwagon.
That said, it takes time, money, determination and organisation to setup your own business, so you have to give them kudos for that and wish them the best.

The speed is what I'm referring to. I think that's what works in its favor, really. Nothing beats a proper, full-fledged guildsite/forum for maintaining a formal raiding schedule, but it's hard to let people in-game that might be relying on you know of real life issues without logging into the game. It's hard to post to guild forums and websites when you don't have a computer, while you can tweet from just about any modern cellphone. I'm not suggesting it's going to replace a proper guild site, or the ingame calendar, or ingame chat, but it might prove to be handy tool to have.

An example of the situation I mean would be just the other night, when my internet connection died on me for about ten minutes in the middle of our Naxx run. Since my GM is in another country and can't call me, and I don't really know any of my other guildies that well to give them my cellphone number, I was completely without a method of contacting them. If we had a guild Twitter set up (the suggestion has arisen), I could've tweeted from my phone about what had happened. That's just one example my sleep-addled brain could come up with for how useful this kind of thing would be.

A wow-based Twitter has the added bonus of being separate from your "real-life" Twitter if you have one. Your entire group of friends doesn't need to know that my connection died...just my guild. Hopefully some kind of cellphone-based feature will crop up in the future to make this really worthwhile. Hopefully before the real Twitter slaps them down for using the name.