Ok i tested it and i knwo the problems

I have always used Blender 2.49 and FBX , not above to work with 3DGS for animated models.
I have tested once some last versions but FB failed, so i can't guarantee above version works ? perhaps yes, just need a little test.

Now your model.
Your model uses a special animation system : IT'S NOT TRADITIONNAL BONES.

I tested :
- Blender 2.6 :
It works well , in Pose mode i can do poses animations
- Blender 2.49 : This advanced animation in 2.6 system seems no more completly compatible with 2.49 :
1) some vertex where not weighted enougt, so big ugly deformations
2) some rotations on some gizmos worked very bad until certain little angle

What i recommand :
Just use models with simple Bones system and armature.
Or choose another animation software for FBX with 3DGS.

If you would use that advanced system but created under 2.49, perhaps it could work with FBX export.

But don't export FBX animated models from Bleder2.6 version with that special system, use bones instead.