This article covers how users who do not have a Skype for Business account can attend a Skype for Business meeting using the Skype for Business Web App. Minimum hardware/software requirements: Windows 7 or Mac OS X 10.8 with Internet Explorer 11 or Firefox 12 or Safari 5 or Chrome 18. And yes, this is my personal Mac, normally without a fat S4B client installed. Right now, I have managed to workaround this by actually installing a fat S4B client, and started an evaluation account with Office365.
I had some strange problems with Skype and Office 2016, too.
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.
Download Skype Meetings App Mac
Once you removed that feature, you should be able to run the web plugin, that usually is deployed, when you open a meeting.
Maybe that link helps with getting the right installer:
Trouble installing the Skype for Business Web App plug-in?
Skype For Meetings App
Hope it helps ...