The application itself is completely separate from Sitefinity and as long as you have access to a Sitefinity site which has the DAM module installed, you can connect from each computer which has the desktop application installed.
As far as your problem is concerned, there seems to be a security issue regarding the installation or at least that's what the message tells me. Are there any specific security restrictions on the machine you are trying to install the application?
Also, installing the official version of the application (link here
) requires .NET 4.5 and usually if you don't have it, installation will be prompted. However, sometimes older versions could cause conflicts.
I would suggest you to try installing the application on a different computer and see if you experience issues again. This way we would be able to determine if this is a specific client related problem.
I hope this information helps. Please, let me know if I can assist you further.