The table tool which you see is same used across MS Office Products say Word. This table structure provides only Sorting facility not Filtering. This behavior being common across all Office products. Filtering is a facility which is exclusive to Excel tables only.
Now this table can be sorted through right click > Table apart from Table Tools (Layout)
If you need Excel like functionality, I would recommend that you convert your table to Excel table. Convert to Excel Spreadsheet appears in both Table Tools (Layout)as well as in Right Click also.
There is already a feature request for this @ Uservoice. Would recommend that you should also go there and vote and put comments. Uservoice is the platform where Microsoft takes ideas from users of its products.