Kendama is a skill toy with 3 different cups, a spike, and a ball on a string. It belongs to the family of catch-the-thing dexterity toys like ball-and-cup or ring-and-spike toys. However, this example is much more involved. Watch closely and you will see that every part of it is carefully engineered. The ridges and hollows aren't idle decoration; they allow a skilled user to catch and twirl the toy or catch the ball in less-obvious places. The thing is perfectly balanced too. It takes a lot of thoughtful refinement to make a gizmo this good.
Accessibility: This toy comes strung for right-handed use. It can be restrung for left-handed use. A better design would accommodate both in the same mode, because this version cannot support ambidextrous use the way a butterfly knife can. Likely the handness relies on whether the string is S-wound or Z-wound. I would therefore look into using a round-woven cord or a solid polymer cord to avoid that limitation.
If you're looking for a large-motion fidget, a kinetic toy, a hand-arm flow exercise tool, a dexterity therapy tool that isn't boring, or something that uses similar manipulation skills as a butterfly knife but isn't sharp, this looks like a good choice. Also worth considering if you have tribal or other ethnic friends whose traditional toys include catch-the-thing toys as many do; they might be intrigued by a more complex version.