The error message of the operating system states "this version [Windows 10 Cloud] was made to help protect you and your device by exclusively running Windows Store apps", which confirms rumors that Windows 10 Cloud will exclusively run Universal Windows Platform apps from the Windows Store.
As this is just an early version of Windows 10 Cloud, I don’t think it would be ideal to claim that Windows 10 Cloud won’t allow users to run Win32 apps that were downloaded from the Windows Store. It’s possible Microsoft will allow this to happen in the near-future, but we’ll have to wait and see until Microsoft officially releases this new version of Windows 10.