Skype hasn't exactly been able to take advantage of mobile growth, and they are even one of the last companies to bring video-chat to the Android platform. You'd think that the company who is leader in the desktop world for video-chatting would know better than that.
But at least it seems they are working on it. Back in May when they finally launched a Skype app for all users, although an underwhelming one, they promised that they would implement video-chatting into their app by the end of the year. Not much time is left till the end of the year, but they've just hired 20-30 Android and iOS developers, so maybe we can still see video-chatting on mobile Skype in time for holidays.
Skype is big, and it's used by many people for the purpose of video-chatting, however, I'm not so sure that 3rd party apps will dominate the mobile market. I think apps that are highly integrated with the OS will – like FaceTime and Google Talk Video that it's supposedly coming to Gingerbread. It's much easier to do video-chatting with just a tap like you're doing with FaceTime, and I assume the new Google Talk Video will work the same way.