not fake at all, the czech social club is next door associated with the beer garden. It's literally their beer hall but open to the public. I don't know how much more authentic you can get outside of being in the Czech republic. You want fake beer garden go to studio square on 36th & 36th. Super nice, but about as authentic a beer garden as cheeze-wiz is cheese.
Speaking of the place, 4 years ago when US was in the WC.......... super effin packed. Great atmosphere 99/100 rating, they'd get that last pt if they only let me bring my dog inside.