He probably thought he had more time. The entire attack plan was to create chaos and confusion. People getting shot at all thought there were multiple shooters. That is why two open windows. He had the stairwell next to his door barricaded so he could walk down the hallway. That would get him to the elevators. Or to other tower wings in the hotel. He obviously wanted to get to his vehicle and expected them to eventually track him down. He had lots of ammo in car and explosives.
Movie cops are morons with slow reflexes who can't think their way out of a paper bag. Real life cops are not like movie cops. He probably got over-confident, and slacked off on the planning.
The funny thing is that auditors are supposed to be meticulous. Of course, most auditors are also fairly good at math, and don't hand their hard-earned cash over to casinos by playing their mathematically-rigged games. So the guy's habitually and irrationally over-confident about his abilities.
This may be right. The Sheriff said when the security guard came on the scene what piqued his interest was that the door was ajar(!) to Paddock's room.
Paddock may have been just about to slip out the door and down the stairwell when the security guard happened upon the scene.
Perhaps Paddock was monitoring police transmissions and thought he was getting out just ahead of the police, but waited too long.