I downloaded the latest Elgato software but when I try to open it, it says there is no specific app for it to open.
You receive this message because the package you have saved must have been corrupted. In this case, I advise you to use the official download URL to download the application: http://files.elgato.com/thcdownloads/egc/GameCaptureSetup_2.00.70.msi
It's recommended disabling any download manager in case you have one. This way you will have a clean package ready to be installed. It should work with the package supplied above.