Try right-clicking on the .dmg and choosing Open. A dialog box might warn you that it is from an unidentified developer. Click Open.
Make sure the time and date are set correctly. If they are off by too much, you might see that error.
If you haven't restarted, try that.
Try booting into Safe Mode and download it there. Just booting into safe mode and restarting normally may clear some caches that are causing the problem. Use safe mode to isolate issues with your Mac - Apple Support
While it is not an App Store app, try logging into your App Store account and make sure there are no User Agreements or other such nonsense waiting for your approval.
I'm not sure if this will work in Mojave, but maybe worth a try:
Open Terminal and copy/paste in this command. Leave a space after the command and drag the .dmg file into the Terminal window, then hit return.
xattr -d com.apple.quarantine
That will try to remove Apple's Quarantine extended attribute. I tried to remove one in Mojave for something else and it failed.