I am experiencing the same issue. I, as the original poster, am on Windows 8.x & earlier today I installed Opera Beta (to test it) & it asked me if I wanted to set Opera as the default browser but Opera Stable was not in the list (Opera beta was tho...)
I have IE11 set as my default for the "Metro conveniences" that come with setting IE as such. The only way I can set Opera Stable as the default browser is by navigating to "Control Panel\All Control Panel Items\Default Programs" through File Explorer... Fix it Opera?