The linked photo shows someone who is being denied entry into the system, i.e. payments cannot be made and thus that one partial inwards rotation cannot happen. Outwards rotation, however, remains unaffected; if they were on the other side of the turnstile, they wouldn't be trapped inside; they'd still be able to exit through the turnstile.
This is different than systems like London and Tokyo, where you pay for the distance you traveled, and a station evacuation mandates opening the fare controls to let people exit more quickly. For better or for worse, that option has never existed in New York.
Gate lines in the UK are manned, if there isn't someone available to supervise the gate line, the gates are left open.
There is no "red emergency stop button" on the gates. Perhaps if the maintenance controls are open there's a red button inside somewhere, but that's not what it's for. Most likely you're remembering other emergency stop buttons you saw, e.g. on escalators or in lifts?
"NYPD say no access"