As per the description above, you want to download and install Adobe ExportPDF service on your computer, Is that correct?
Adobe ExportPDF is an online Document cloud service online service which cannot be downloaded as an application on a computer. But we can access the service through a browser and can be accessed through desktop and mobile app Adobe Reader DC.
Access the service through the URL https://cloud.acrobat.com/exportpdf with your Adobe ID and password on a browser like Chrome, or Firefox, or Safari.
You can also access the service through the free desktop version of Adobe Reader DC, just sign in with your Adobe ID and password, download Adobe Reader DC from Adobe - Adobe Acrobat Reader DC Distribution
For troubleshooting, you can refer to Troubleshooting Create PDF, Export PDF, Adobe Send, Fill & Sign … services(PDFPack or Document Cloud...
Feel free to update this discussion for any further assistance.