One guess is that the particular hotel they're at is actually not pet friendly, and he's got his cat stashed away in the bag he's carrying to smuggle it into his room.
She asks him why he used Priceline Express Deals to book this "fabulous" hotel. He replies that he's able to see if a hotel's pet friendly AND he can get a great rate without bidding. She then asks where his "furry friend" is. His demeanor when he tells her he doesn't have a cat suggests to me that he's nervous about the question because he's got a pet with him even though he's not supposed to. When you watch it again notice how he looks into the camera and stutters the answer. IMO that has "guilty" written all over it. If that is the punchline of the commercial, it would've been more catchable had there been a muffled "meow" coming from his bag during their silence after he answered her. Then it's revealed the hotel isn't a pet friendly one but he booked the room anyway because of its low, bid-free rate.
My other guess is that he's just a wacko who's obsessed with cats, so much so that he likes to stay at pet friendly hotels. That would justify the stuttered answer and awkward silence - He realizes she's gonna think he's a weirdo for preferring pet-friendly despite not actually owning one, and she's thinking exactly that. That would also explain all the cat related crap he has, such as the shirt and the magazines.