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.

Skype For Business Outlook Plugin Download

Once you removed that feature, you should be able to run the web plugin, that usually is deployed, when you open a meeting.

Skype for Business is an instant messaging client, a collaboration tool with a main goal to provide users with chat, video and audio calls. Highlights: Powerful collaboration tools for real-time input - record meetings, share your screen, and annotate PowerPoint for real-time collaboration with up to 250 people. Just like Skype does with its desktop client and its Web App, also known as Skype for Web, Skype for Business supports a wide set of connections modes: A fully-featured desktop client shipped with the Office 365 suite: this is easily the best way to use it if you plan to host Conference Calls – assuming you’re willing to pay the required fee. Skype for Business (SFB) Web App is almost identical to the meeting experience offered by the full version of SFB. If you received a Meeting Invitation for a SFB Meeting and you are a student, vendor, contractor, guest of UH, or simply don't have SFB on your computer - download and install SFB Web App to experience a Lync Meeting in a web browser. Learn to use the Web Meetings App!

Skype For Business Web App

Maybe that link helps with getting the right installer:
Trouble installing the Skype for Business Web App plug-in?

Skype Web App Plugin Install

Hope it helps ...