Hi,
thanks for your post, and sorry for the trouble.
This is indeed really strange. The HTML code for your links is correct, and if JavaScript is turned off on the page, the links work fine. My assumption therefore is that there’s some JavaScript code on the page that is influencing links, but that’s somehow broken (for example some JS that counts clicks for statistical purposes).
To be sure that this is not caused by TablePress or its included DataTables JS library, please temporarily uncheck the “Use DataTables” checkbox on the “Edit” screen of the table.
If the links still don’t work after that, the cause for the problem must be in some other JavaScript that is loaded into the page, e.g. by your theme or another plugin. In that case, you’ll need to temporarily deactivate other plugins one by one, and switch to the WordPress Default theme TwentyTwelve, until the links work.
Regards,
Tobias