The ‘Target Platform’ dropdown box only contains Linux and OS X. Restarting Unity doesn’t help. I’m using 5.2.1f1 on Windows 8.1.
Try updating or reinstalling Unity.
A missing target platform give me the impression a playback engine is missing from your system. Why that would happen is beyond my speculation and it’s a very crude guess.
Unity 5.2.2 and 5.2.3 have some fixes regarding Windows, although I found no specific change that precisely said “fixed target platform dropdown”.