There are no games that require exactly DX11.1 to run. Anyway Dota is a mod of the super old Warcraft III which only requires DX9.
If you are getting DirectX related error messages (it will say something like "Direct blahblablah crashed/failed to initialize or is missing") then you got corrupt or missing DX files.
Download and install this to restore core DX fileshttp://www.microsoft.com/en-sg/download/details.aspx?id=8109
And then this one to make sure it is updated to the latest version your OS supportshttp://www.microsoft.com/en-sg/download/details.aspx?id=35