This actually isn’t a bug. OneDrive / SharePoint just doesn’t support the use of office clients when using anonymous links. I believe the team is looking into adding this support at some point but you must use the office online web clients for anon links.
It's an undocumented, incomplete roll out of a feature. Someone stuffed up because literally 99.9% of users use the desktop apps. So why make a feature useful for 0.1% of users? Please fix Microsoft!!!
Chris is correct. The Office desktop apps don't currently support opening the anonymous/anyone links though this is certainly something we are looking at solving. I do want to note as well that once a signed in user has used the anonymous link, they are "redeemed" on it and should be able to open the document via the desktop apps. Hopefully that helps! Thanks!