Fairly sure that they ask that your dog is well behaved around others, doesn't bark/fight/is house trained and if you show up and that proves not to be the case, you'll be asked to leave.
It is a novel concept but I believe they also apply this to humans, asking that people behave nicely in the cinema and ejecting those who fight/shout/piss and shit in there.
From friends who have been, the screen is not sold out and they space people out a bit so theres room on the floor for the dog. Small dogs on laps is expected, but dogs on seats is not.
People also tend to take their dog a blanket/bed to lie on, as the flooring is rarely as comfy/padded as carpet at home.
As I said before, cinemas are not doing this because they love dogs or feel sorry for people who have dogs with separation anxiety. They're only doing this because they need to keep their businesses afloat and the Doggy Pound makes it worth the extra cleaning and organisation.
If you hate the idea, tell your cinema and back that up by going to the cinema (on other days!) and spending your money there rather than staying at home.
Would love to know how many people objecting to this actually went to their local cinema in the last 12 months more than once.