I had some strange problems with Skype and Office 2016, too.
Skype for Business on Mac, Lync for Mac 2011 and Communicator for Mac 2011 users can't control desktops shared by Windows users. This also won't work for Skype for Business Web App on Max OSX. For Skype for Business Online, this feature requires Microsoft PSTN Conferencing, Exchange Unified Messaging, or a third-party audio conferencing provider. If the Skype for Business desktop version is installed, you can perform the follow steps to join the meeting with Skype for Business Web App. In the meeting request, right-click or tap and hold the Join Skype Meeting link, and select Copy Hyperlink.
The solution was easy: Office 2016 (Professional Plus in my case) installed its own Skype for Business software, which block the execution of the 'SkypeForBusinessPlugin.msi'
When you open 'Apps & Features' and choose 'Modify' , you should see 'Skype for Business' in the list.
Skype For Business Web Plugin
Once you removed that feature, you should be able to run the web plugin, that usually is deployed, when you open a meeting.
![For For](/uploads/1/2/4/3/124395212/819287356.png)
Download Skype For Business Web App
Maybe that link helps with getting the right installer:
Trouble installing the Skype for Business Web App plug-in?
Trouble installing the Skype for Business Web App plug-in?
Skype Web App Plugin Install
Hope it helps ...