What is the single word for this style of mixing?
"Pouring from a height" seems to be an accepted terminology; I don't think there's a single word for it.
In the Navy, it is called "boxing your coffee". This is a pun on boxing your compass, which in this case means to sail back and forth between known points to calibrate the magnetic compass.
Boxing your coffee: Using two paper cups and pouring back and forth to mix creamer and/or sugar.
"Boxing your coffee" Wiktionary, Appendix: Glossary of U.S. Navy Slang
https://en.wiktionary.org/wiki/Appendix:Glossary_of_U.S._Navy_slang