OK
I'm Belxanthian and I'm the main developer for Ready to Play so I hope that means your in good hands
Ready to Play uses "mostly" the registry to store its data. The key that stores the window position is
HKEY_CURRENT_USER\Software\Stardock\Ready to Play\MainWindowPosition
If you could please use regedit and delete that field then run Ready to Play and see if it will now remember your position. If it doesnt we will have to dig into whats special about your system to find the problem.
Good Luck
Belxanthian
Hi there,
So I now understand what where the Belxtest (or something like that) appearing in the friends list 
Delete the key you mentioned and then I got this at first start :

Exit the program, launch it again...this time it works, I have the main window. Position it where I want it to be (top right of the screen), then exiting the programe (left click in systray, exit)...and it is still in the middle of the screen 
Here's the registry key value : "540;215;360;440"
From what I can read, the value should be more like 1080;0 for the 1st 2 digits ? So it seems that it's not registering.
Then we have the problem of the LastFullWindowHeight key, which stays at 440 even though I try to set it to nearly 700 every time.
Trying to modify those values by hand...will report back when it's done.
[Edit]
Nope, even changing those variables by hand didn't help. Still in the middle. It's weird. If you want I can set up Teamviewer so you can drop by and see directly what's going on ?