The weirder thing about that claim is if China is arming both sides, then how are they a puppet master? A puppet master chooses who wins and who loses to control the puppet. If they’re not choosing a side, then they’re letting the combatants decide for themselves. The exact opposite of a puppet master.
You could argue China is an agent of chaos as they’re letting things play out however it will play out. But puppet master is hilariously wrong by even the most casual observation.