I don't think this is exactly possible via the Field Rules, but here's a way to do it via Javascript.

1. Turn off back-end validation on your form.
2. Add a custom HTML element to your form.
   • The contents of the field should be:   {/_currentuser_display}
   • The field should have CSS Class of:   currentUser
   • You can hide this field via Field Rules or CSS.
3. Then your User drop-down field in the table should have CSS Class of:   currentUser
4. Add the following Javascript to your form:

$(document).ready(function() {
  
  //When the form is loaded, loop through each row of the table and check if the drop-down
  //field with the myTableUser class matches the current user (a custom HTML element with
  //the currentUser class).  Hide any rows in the table where the user name doesn't match.
  var currentUser = $('.currentUser').text();
  $('.myTableUser select').each(function() {
    if($(this).val() != currentUser) {
      $(this).closest('tr').find('*[required]').each(function() {
        $(this).removeClass('required')
        $(this).removeAttr('required');
      });
      $(this).closest('tr').hide();
    }
  });
  
});

Without the Javascript, the table has all its rows:

But with the Javascript, only the rows with my name show and are required:

Note that the code only runs when the form is loaded, so if I change one of the user drop-downs, it doesn't hide that row immediately.  We can modify the Javascript if that behavior is needed.