Automation using counters

No, not like this. I would do something like this:

Create a counter and a timer:

counter:
  stairs_motion_count:
    name: Stairs Motion Count
    initial: 0
    step: 1

timer:
  stairs_motion_timer:
    duration: '00:01:00'

One automation to reset the counter when the timer finishes:

- id: '1576869751187'
  alias: 'Reset counter when timer expires.'
  trigger:
    platform: event
    event_type: timer.finished
    event_data:
      entity_id: timer.stairs_motion_timer
  action:
    service: counter.reset
    entity_id: counter.stairs_motion_count

And then one automation that increments the counter, starts/restarts the timer and executes another action in case the count is > 1

- id: '1576869741194'
  alias: 'Increase Counter and start/restart timer on motion'
  description: Motion in Stairs Counter
  trigger:
    platform: state
    entity_id: binary_sensor.commonstairs_movement
    from: 'off'
    to: 'on'
  action:
  - entity_id: counter.stairs_motion_count
    service: counter.increment
  - entity_id: timer.stairs_motion_timer
    service: timer.start
  - conditon: numeric_state
    entity_id: counter.stairs_motion_count
    above: 1
  - action you want to do if count > 1
     

This can be simplified If you can change the time the motion sensor uses to change from “on” to “off” when there is no motion.