AC Line Splitter - How does it work? Checked with a Fluke 324 & Hioki 3288-20 Clamp Meters [CC] 

You're welcome!

I don't know who coined the term "line-splitter" for this device but that designation does not mean "split-phase" in the sense of 3-wire single phase system. It simply provides a physical separation between the two single-phase voltage supply lines. This allows for the convenient clamping of a clamp meter on just one line of that supply through one of the legs of the line splitter. As you know, with a clamp-on current sensor, you can only measure current on one line, not two. In this manner you can connect any single phase power cord for small appliances at the output of the line splitter without physically altering the cords themselves, and then measure their current by clamping on a leg of the line splitter.