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I haven't used the Headlines module myself, so I'm not sure I can assist here. I also am not sure I understand what your issue is at this point.
However, I will point out that you are using an older version of XOOPS - 2.0.13 (assuming that since there is no 2.13). I have a copy of 2.0.13.2 I looked at. There is no class/theme.php file in 2.0.13.2 but there is in 2.0.17 and .18, so I expect that is a big part of the problem (based on the error issue), but not knowing the Headlines module, don't quote me.
You might want to update to the latest version of XOOPS and then see if you experience the same problem. Note that you need to follow the instructions carefully as there are some updates that need to occur to the system along the path.