Now that I think about it some more, my answer was wrong. I tried to set it up as an analogy to a dynamic absorber (the dynamic absorber was shown in slide 3 of the electrical analogy to vib thread).
But the problem here is that there is another element Zk1 connected to the node between Zm1 and Zk2. The short circuit path through Zk2 and Zm1 does not drag that particular node to zero voltage (zero velocity). So the current (force) flowing through Zk1 is non-zero and we can’t ignore the presence of Zk1.
In contrast, the dynamic absorber equivalent circuit has extra elements Zk1 and Zm1 that we can ignore, but we can ignore those because they are connected to a node that is dragged to zero voltage by the short circuit Zk2 + Zm2.