Does this ignition switch look correct?

Usually, if the lock cylinder pulls right out of the switch without having to depress the button, the switch housing is usually bad. Just aluminum or pot metal switch housing, so, it wears out easily. '69 uses a unique ignition switch, lock cylinder, and bezel. The $20 one you linked to is not for a '69 model, it's for the '68 and earlier ones.
Yes I didn't order that. Order these instead

FITS 69 Roadrunner Charger Coronet Dart Ignition Cylinder Key Switch Lock Repl. | eBay

Mopar 69 Coronet / Superbee Charger Roadrunner GTX Dart Ignition Switch 1969 NEW | eBay