关节 here means 'connection' or 'pivot point' in a network of influence — by Ming and Qing times 卖关节 already meant 'to sell one's connections', i.e. take bribes to clear a path through bureaucracy. It's a classic literary term that survived into modern Chinese.
register
Sounds slightly literary/old-fashioned — modern news reporting prefers 受贿 (shòuhuì, accept bribes) or 行贿 (xínghuì, offer bribes). Use 卖关节 for color or in historical contexts.
