Maybe I'm a bit confused, but I didn't find anything in the forum to help me...
Is there a way to play WL on Microsoft's OS like W8 or RT?

I don't have a Surface, but from what I understand, it should work fine. The Surface RT originally didn't support Flash, but they added it later. See http://allthingsd.com/20130312/back-in-a-flash-with-flip-flop-microsoft-now-supports-adobe-in-windows-8-windows-rt-browser/

Go vote for the Windows Phone App in Uservoice, then you can use it in Windows 8 without any problems :D

I spent almost all day trying to resolve the problem, but still can't play on surface...
There are plenty of suggestions on the net, but no one works on my device.
But thanks for your reply!