Yep, you are indeed supposed to report and pay taxes on all gambling winnings.
It's not something I'm personally doing.
Incidentally, it's probably a +EV idea for civilians to keep track of their wins and losses during the year. Because they might hit a jackpot, which will be automatically reported, and they'll want losses to offset it.
Since we're all theoretically playing a winning game here, accurately reporting results would just add even more to the tax burden.