Very few (if any) things in life on a non-quantum scale are actually random. Roulette results, dice throws, shuffled cards, etc, are all the results of complex and hard-to-predict processes, but they are no more random than the markets.
What people mean when they say that something is random on a non-quantum scale is this: the process is so complicated and hard to predict that our best models of the process incorporate a significant amount of randomness.
This is the case for markets too, where a multifractal random walk is about the best model we have.
I suspect a better definition would be a wager based on random chance. Markets aren't "random", they are just suitibly complex enough to seem like it. Some people apply algorithms and emotional analysis to predict behavior. This might sound like poker, but I would argue all of the influences in a market are clearly visible. In a game of chance like poker, card ordering is still random (yes you have probability of predicting next card, but you can't see it until it happens).