The animations themselves don’t actually move characters around in the world space. They make the motions of movement, but then you need to write code that actually tells them to move forward. Here’s a video that might help:
@ mentioned that animations don’t move characters around world space, but this is only partially true. Animations can contain root motion data, which can be used to interpret movement of the rig’s root node into world space movement. You do not necessarily need to write all the movement code to get your character translating in world space.
I took a look at the spider model you linked in your post and it does not have any root motion in the animations. There is nothing wrong with what you see in the import settings for the animations. Those areas are supposed to be green…red would be bad. So, although you have no root motion data now you can add it yourself with a little bit of work.
Here is a quick overview of how to author root motion in Unity:
For this asset you will have to duplicate the Walk and Run animations so that you can edit them. Simply select each of those animation in the project view and use CTRL+D on Windows CMD+D on Mac to duplicate the animation into a Unity animation clip. Add these new clips to an AnimatorController and when you open the Animation window, both will be editable. I recommend moving the transform on the last frame of the animation only (Unity will handle all the calculations from the start point to the end). I only took a short look at this asset, but it should not take too long to get it looking nice.
