It sounds like a mistranslation of the word "thing" or perhaps a secondary unknown meaning of the word. Perhaps the joke had a physical portion, a slight of hand or a look over here while i grab a drink of your beer type of visual pun. A joke not meant for the person it's being told to but for those nearby watching.

In ancient Sumeria, taverns were plentiful, always run by women, and sold beer brewed on the premises. The stock of beer would range from simple mash to luxury drinks, laced with herbs and honey, with correspondingly different prices. Most Sumerian jokes featured dogs, so that is just a red herring. The joke is that the dog does not distinguish between the el cheapo beer and the most expensive brew, suggesting, wryly, that the distinction is an illusion designed to wrangle money from patrons.