I understand you're looking for a DirectX 8.1 offline installer, but I need to provide an important clarification first.
DirectX 8.1 is already included in the base installation of Windows XP, so no separate download is typically required for that OS. download directx 81 offline installer link
If the game still says d3d8.dll is missing, manually register it: I understand you're looking for a DirectX 8
Practical Notes
Legacy Games and Applications: Some older games and applications were developed with DirectX 8.1 in mind. These applications might not work properly with newer versions of DirectX. download directx 81 offline installer link