Here is the solution to what was going on;
I use Launchy (2.5/2.6b doesn't matter) with Alt+Esc as the hotkey for activation. This apparently does not make Windows 10 happy. It worked fine with Windows 8, Windows 7, Windows Vista and probably XP before that (long time Launchy user).
If I change the Launchy hotkey to for instance Ctrl+Space or Alt+Space, Alt+Tab keeps working as expected.
I know that Alt+Esc has an action attached to it in Win10, but I did not realize it would react like this to having one of the hotkeys overwritten. So I dunno if this would need to be "fixed" in Win10 or in Launchy - neither is very likely anyway so I better get used to the new key combo.