I did look at the source to that page and didn't really see anything that jumped out at me as an obvious way to identify this table.
So the table lacks an id? That might explain numerous tables in that page. If a table lacks an 'id' attribute then it also won't have an id. Are you sure this is a unique property of the table you are after?
The point I'm trying to make is that you need to find what, exactly, can consistently identify the page elements you are after. Until you know what that is, there's really no sense in writing any code.
The approach you suggest -- to find a table with an empty id attribute -- might be more easily found using [man]preg_match[/man] than using DOM to parse the entire document.
If, on the other hand, you said "the results I want are in the 3rd row of the 2nd table of the page. The first cell in this row contains a nested table with only 2 rows and I want the 2nd cell in each of those rows" then DOM might be the way to go.