Hi Jamie,
I reviewed your file and can see why the tables don't show up in the Name Manager and my code didn't count the tables.
I had assumed that these were ListObject tables, which can be created by:
Selecting a valid range then from the Ribbon > Insert > Table
These ListObjects were called Lists prior to xl2007, and they are now commonly referred to as "Tables".
ListObjects show up in the Name Manager and you can filter the Names to just show "Tables".
What you have in your file are not "ListObjects" but rather "Data Tables" (Which is exactly what you've correctly called them from the beginning, so the misunderstanding is mine!)
I haven't had experience with Data Tables, so I appreciate that you've helped me become aware of them.
In Excel 2010 Tables can be created from the Ribbon through Data > What-If-Analysis > Data Table...
This link provides some instructions
Calculate multiple results by using a data table - Excel - Office.com
So now that we understand why the Name Manager and ListObject Macro didn't work, we can revisit the problem you are trying to solve.
Here's my uncertain understanding and I welcome corrections from others who have more knowledge on this:
Data Tables are not Objects within the Excel Object Model, so they can't be easily counted or listed the same way ListObjects, PivotTables or Shape Objects can be handled with VBA. Rather they are Array formulas that use the TABLE() function leaving a formula that looks like {=TABLE(,B7)} where B7 is the "What If" Column Input.
One approach to counting/listing the Data Tables could be to use VBA to search all formulas and gather unique instances of "TABLE(*,*)". That seems more complicated than it should be, so I'll wait a bit to see if someone else can share a better approach.