Almost sounds like some antivirus software might be blocking the updated version somehow.
Can you try to update your antivirus definition, if you have one installed.
I mean, nothing should mistake it for something malicious (https://www.virustotal.com/gui/file/94aeb36dd4f16224f8b014c96fc74628a16bc1f7d0637dc8847e6a4ba228d048/detection) but you never know.
The changes between the version you download and install from the website, and the update is very minor. If the one you install from the website is working fine for you, i would just wait to update until the next one.
Should be another minor update within the next week.
You could also try downloading this file: https://www.equalify.me/dl/beta/dsound.dll
and place it in the %appdata%/spotify folder. Overwrite the dsound.dll that is already there.
Close Spotify before replacing the file.