Only present in 'Team Work' and 'Active Work' as it's where it makes most sense. Should you already be the assigned user the quick icon will not show.
Once clicked the logged on user will be the assigned user and there will be a record in the action log.
Currently only tested in my lab environment but seems to work with all browsers and supported work item types.
I've attached the files needed in a zip archive. To install just drop the files in CustomSpace (merge custom.js if you have other stuff there already!)