A good picture for this word is a ring of chairs with one chair missing. People keep circling while the music plays, and the moment it stops everyone drops into a seat — except one person, because the seats were short by one from the start. All the walking changes nothing about that shortage. Both uses of the phrase keep the same shape: constant movement, a fixed number of seats, somebody always standing.
Two branches
遊戲本身
這一家就是核心畫面本身：真的有椅子、真的有音樂、真的有人被淘汰。
noun · B1
A party game for children in which the players walk around a row of chairs while music plays; there is always one chair fewer than there are players, so when the music stops and everyone sits down, the player left standing is out.
搶椅子（遊戲）
職場上的換位子
把遊戲搬進辦公室或政府：人一直換位子，位子的數量卻沒有變，所以動作再多也解決不了原本的問題。
noun · B2
A situation in which people keep moving from one job or position to another for no good reason and with nothing useful coming out of it.
人事大風吹；無謂的輪調