I think the term "market" comes from the fact that it uses stock market–like pricing and allows you to sell your bets at any time. Ie. you buy "shares" of some outcome for 0.3$ if the probability is 30%, and then if the probability at any point goes to 50%, you can sell the "shares" for 0.5$ each.

(Which of course doesn't make it any better or less of a casino, this is just to say that the word market didn't come from nowhere)