On a motorbike a steering damper increases the resistance to the turn of the handlebars. It 'damps' the action, used mainly to stop 'tank-slappers'; an extremely violent shaking of the handlebars that can result in death.
Not ever experienced anything, anywhere like a 'tank-slapper' on my MTB,
so can't imagine what or why you would fit a steering damper to a push bike;
maybe if you are doing extreme stunts and drops it could be useful in preventing the handlebar being wrenched out of your grip if you ballsed it up? :?