Hello,
Sorry to hear you are having issues. But, I can not reproduce your issue on my system. I tested on my system and download a really big file. 100G. And set my Deskscape to have my playlist of changing wallpaper as a screensaver. But, no issue, the download still carry on while the screensaver run changing pictures every few minutes.

Perhaps something else is causing it. First, please try purge and reinstall Deskscape steps as mention here : [Link]. Just make sure to redownload the latest version from your account page. Reboot after the purge. Reinstall and reboot again after the installation. Retest and report back here.

Thank you,
Basj,
Stardock Community Assistant.