From ESRI support:
Thank you so much for your patience while I worked on this case. It took a lot of testing but I was able to determine the issue with [the lines] that did not work with the Split Selected Lines tool. It turns out that for those 4 problem lines, both segments are true curves. It not apparent at first because the second segment is so short and flat, but if you edit the lines and extend that segment, you'll find it is a curve. For some reason, the Split Selected Lines tool does not like multi-segmented lines composed of 2 true curves and so it generates that incredibly unhelpful error. I have logged a bug for this issue, stressing both the underlying behavior and the bad error:
BUG-000098306 [Split Selected Lines tool fails with error "The Geometry has no Z values processing feature OID:" when the multi-segmented line is made up of only 2 curves.]
You can check on the status of this bug at any time by logging in to your My Esri account and checking in the Support section (My Organization> Support). A workaround for your situation would be to replace the second, short curve segment with a straight line segment. You can do this with the following procedure in an edit session:
1. Delete the end vertex of the problem segment, so the line becomes just one true curve
2. Create a new straight line at the end of the curve in the same shape as the old curve (they will be 2 separate lines)
3. If desired, use the Merge command from the Editor drop-down on the Editor toolbar to make them one segment
Though given that the goal is to break up multi-segmented lines, you may want to leave the curve and the straight line as two separate lines. In any case, I hope that answers your question. As this behavior is a bug, there is no further troubleshooting I can offer. So I am marking this case closed.