I bet this program has a setting to delete instead of moving it to the recycle bin.
If this pc is only used for PlaysTV, you may want to consider disabling the recycle bin, which deletes the files directly rather than moving them to the recycle bin.
A third option is to set a limit on how much data can be moved to the recycle bin.
Altering settings for the recycle bin can be done as follows:
Minimize all programs so you see the desktop. Right click on the recycle bin and choose properties.
From this dialog you can change the maximum size or disable the recycle bin altogether.