Despite the fact that you selected Excel 2016 when you posted your question, the screen shot depicts Excel 2011. On the assumption that you actually are using Office 2011, the question is, what is the specific update level of your software?
The Solver Add-in was not included with the original release of the program. It was later added by way of Service Pack 1 (14.1.0), so if SP1 has not been applied it would explain the missing .xlam file. [BTW: The current version of Office 2011 is 14.6.4]