First of all, I am terribly sorry for posting so late XD
In order to fix the problem, you simply need to install the latest version of directX. If it doesn't work, ask me for help and I'll be glad to answer you :)
Is the game only compatible with Windows 8 and up? I have the latest directX installed on my computer (Windows 7- directX11) so I'm not sure what the problem is... the missing component error won't disappear.
If you have the lastest version of directX for your windows then there shouldn't be a problem. Did you make sure to keep the files together after you've extracted them in a new folder? The application file "Tyrania" or any of the other files inside the zip should always be together in a folder.