Hi retro30,
Thanks for the file.
The core of the problem is certainly how the Editor View works. Go with your animation by moving the time slider to any new position. Now, press the A key, and again. You will notice that the Dynamics that you have set up in the IK will continue to deliver new positions.
The editor view updates the scene more often, the renderer (Picture Viewer) will not.
On top of that, your scene has the cape above the cube, it should be below the cube to have all the information needed when it is calculated (Priorities).
To see your scene correctly even while moving the time slider, the cube needs a Point Cache (Object Manager> Tag>Character Tags). Initiated and calculated. The Skin object needs to be disabled after doing so. Then the cape needs a Point Cache, this one needs to be initiated and calculated as well. The Cloth must be disabled now. Skin and Cloth would add more information than the cache already provides at that point.
The faster way to see if it works would be with the Render>Make Preview (All Frames).
The chain of information flow from Root animation, to IK to Dynamics. From there to Skin and the Cube. The Cube is then used as Belt. This information is used to bind the cape. The Cape uses this information to react while using the cube as collider. It is easily to image that any jump or repetition (viewer refresh) of a single step in this process chain will cause trouble. On the other hand the editor view is refreshed often and ther is the core of the problem. Cache takes this problem out.
Cached file:
https://www.amazon.com/clouddrive/share/JFuTAsLPGfG4qJQUtmsaKhJxnCJQq8WU8b6fBnao7xe?ref_=cd_ph_share_link_copy
All the best