If you play with a player's card, the casino has an exact record of all of your machine play. If you get rated for comps while playing table games, the casino has an estimate of your wins and losses. If you have played much at table games, you've probably noticed the dealers asking to color players up when they leave the table. Part of the reason is to maintain low denomination chips at the table to minimize the need for refills. However, they also do this to help them judge how much the player won or lost at the table. If gambling income becomes an issue for the IRS, they can obtain these records from the casinos.

I'm sure you are correct that many, many people do not report income that doesn't have a paper trail. On the other hand, if the IRS wants to pursue the issue, they have a number of ways to ascertain someone's income. Sometimes it's just an estimate. But then it is up to the taxpayer to prove that the estimate is wrong. I don't think "innocent until proven guilty" applies here. I could be wrong but I think this is the way it is.