According to the most recent timeline: 
9:59 p.m. Hotel security guard is shot 
9:59-10:05 p.m. Gunman fires at maintenance worker who finds injured security guard, worker tells hotel dispatchers to call police and report a gunman on the 32nd floor 
10:05 p.m. First shots are fired on crowd 
10:12 p.m. Two officers arrive on the 31st floor and determine gunfire is directly above them 
10:15 p.m. Last shots fired by gunman 

The most crucial detail, as far as LVMPD's reaction time, isn't about when the security guard got shot but rather,  when exactly did the maintenance worker notify hotel dispatchers about the gunman. Could it possibly be that he contacted them near 10:05 p.m., just seconds before the gunman opened fire on the crowd? That would have given the first responders under 7 minutes to receive the call, rush over to the hotel and ride the elevator up 31 floors. Another crucial question: When did the security guard notify hotel dispatchers of the gunman? Was it after the fact?