The center/main bone animation is not loaded and the rest of the bones/model is turned in a strange way (but other than that, the animation works):

   
   

Files:
(drop the dae of the mesh and then of the animation on mesh ed)
http://solidfiles.com/d/eGCP
(for pw, check your pm)

Is this because of the model? Or because of the importer?
Do I have to add a bone that doesn't move?

The 2 files have different skeletons,

one has Bip01 bone, the other doesn't have it.

I fixed that, but it still doesn't work:

  soldier.7z (Size: 988.99 KB / Downloads: 8)

Looks like it doesn't load Bip01_Pelvis from run.DAE...

you need to have the same set of bones, the animation doesn't have bip01_pelvis

Yes it does (open the animation file (run.dae)) in a text editor.
It just doesn't load it for some reason...
I think this is a bug with the importer.

but it doesn't have any keyframes, so it's not detected as a bone

you should either:

1.add some keyframes to the bone

or

2. include the mesh in the "running" animation max file (so it contains the skinning information, so the node will be treated as a bone)

(keyframes or skinning)

Method #2 is recommended