As per your account information, you have subscribed to Adobe Export PDF. Adobe Export PDF is an online service that you can access online via https://cloud.acrobat.com/exportpdf
Or you can download the Adobe Reader DC desktop application to access the service through that- Adobe Acrobat Reader DC Install for all versions
in order to activate the service, you just need to "Sign In" using your Adobe ID and password under which you have the subscription registered.
Hope this is would help you activating the subscription on new computer.