The Excel team has made a change in the behavior of certain file types to increase security. This change came in the security updates KB3115262, KB3170008, and KB3115322. Previously, when you tried to open an HTML, XLA, or XLAM file with an .XLS file extension from an untrusted location, Excel would warn about the mismatch between the file extension and content, but would still open the workbook without Protected View security. After the security updates Excel no longer will open the workbook because these files are not compatible with Protected View and there is no warning or other indication it was not opened.
The Excel team has released a follow-up change in HTML/XLS file behavior in the 8/9 and 8/16 security updates for Excel 2010, 2013, and 2016. Excel will warn about the mismatch between the file extension and HTML content, but will now open the workbook in Protected View as an additional layer of security. If you trust the workbook, you can then enable editing. XLA and XLAM files are not part of this change, they will continue to not open in Excel.
How do I get the update? It depends on which version of Office you have.
Workarounds for .xla and .xlam files: https://support.microsoft.com/kb/3181507.