As per the description above, you want to download Adobe ExportPDF subscription on your computer, Is that correct?
Adobe ExportPDF is an online Adobe Document Cloud service which cannot be downloaded as an application on a computer. But we can access the services 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 use the freeware Adobe Reader DC to access the service of Adobe ExportPDF, just sign-in with your Adobe ID and password in Adobe Reader, to download Adobe Reader, use the URL 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.