"Roll 'em" = "Roll them" - which is what people say to the person who rolls the dice in a different casino game, Craps. Saying it to the dealer for poker, a card game, shows Her Majesty doesn't understand what's going on. So the dealer is surprised and baffled ("popeyed") and the gentleman next to her is suggesting she may be unfamiliar with how things are done here.
My guess is the dealer was shocked that Her Majesty wanted to play poker and came at it with such a slang term as roll'em.
'roll 'em' refers to casting the dice in roulette. So it was an inappropriate reference and shows that Her Majesty had done some research but not carefully as she was referring to the wrong gambling game. The Dealer would have been very surprised to hear such terms anyway from the queen