As the game, the interface is probably in a "beta"-state, so maybe some changes are already planned, but anyway, here's my vision of a better interface :
Firstly, I'd prefer a fullscreen interface. With the spare space it would imply, you could merge the Buddies window in the main window, something like this :

See First Attachment
(Somehow I lost the first image, although the only thing I wished to show is still on the bottom of the other image.)

Or something like this.

I don't like the whole fact to have 2 windows opened, it's nicer to have everything on the same page imo.
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Secondly, I don't feel the need to stack another screen on the main one when you start a game and have to choose the type of game, it would be easier to open the "Play Game" window just like the Summoner Profile one. This would look like something like this :

See Second Attachment

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For those "pro" people for whom the whole windowed thing feels just so pro, you can put a windowed mode toggle in the options, which would allow to toggle the Buddies window as a separate window.
Additionnaly, it would nice to use the in-game pointer 'cause the Windows one is a bit silly, and also to use some mood music.

Also, I'm not sure of this, but doesn't a windowed mode uses more memory?

actually, the only thing that worries me with that suggestion, is the problem with the buddielist.
I can hardly sort it as it is, because you have to drag stuff around. As soon as you have a directory with enough entries to fill up the window vertically, the place is getting too small to put the first name in any directory that lies below the screen filling one that you have to drag it out of.

The above suggestion would need a way to move ppl via context menu rather then drag&drop only.
This is convenience I guess.