Generally, SolidWorks launches a miniature version of Microsoft Office that matches the SolidWorks version if you do not have any installed. If you do have a version of Microsoft Office installed, it will use this one. If the design table file was generated on another computer using, say Microsoft Excel 2016 and you're trying to open it through SolidWorks on another computer that uses Microsoft Excel 2014, SolidWorks won't be able to open it because the file will have been saved in a future version of Microsoft Excel.
You can open the file from Microsoft Excel 2014(even though SolidWorks says it can't) and then save it in 2014 and it should work.
In my case, I run SolidWorks 2016 and Microsoft Office 2012. The guy who did my design tables made them on Microsoft Office 2016. I had to open each file and save them as 2012 in order to be able to open them through SolidWorks.
Thanks @Alex for clarification.
In your note you mentioned that if there is no Microsoft Office installed then it picks up miniature version of excel, but in my case where no MS Office was installed intially, design table command was not working at all.
But when I installed MS Office 2013, it started loading the minature excel version.