Excel kept saying that my .xlsx files weren't associated with Excel by default, so I thought to be clever and execute an Office repair action:
Control Panel > Programs > Programs & Features
Microsoft Office 365 - en-us: right-click and choose "Change"
Then you get the choice "Quick Repair" or "Online Repair"
I don't know what choice I made, but what I know, is that my Office installation was completely unusable because:
So, after that, I kep Microsoft SharePoint Designer 2010 - for my much beloved Picture Manager, and I installed the 64-bit version of Microsoft Office as well.