The basic features must include the ability to play real time and the option to put lag tolerant option, saw past games (pgn reader), and watch others play.
Additional features can include pictures or chess sets which will then be stored on the apps cache or permanent folder.
Users may also download their games.
The videos can be delivered (or cached) using different app.
Ofcourse this all can be achieved since those two OSes allow a lot of flexibility in data management and code implementation. Now it is Flash, but Chesscube developers may consider silverlight which can be used with the same experienced mobile and desktop on windows.
The only limitation will only be that people can use their computers to cheat. Well, this can also be done on computer using 2 computers or the other chess apps on phone. The benefits outweigh the (senseless) risk.
End words : It would be nice to spend the time on the road to work, school, on business travels, etc playing chess while drinking coffee.