
Captain Riley |

Just for clarification I assume your asking for the sake of this ability?

Captain Riley |

Though I don't have a hard answer for you, the wording from the Magic page leads me to believe that no, threatening is not interacting:
"Creatures encountering an illusion usually do not receive saving throws to recognize it as illusory until they study it carefully or interact with it in some fashion."
Considering the illusion isn't doing anything to them directly, simply allowing you to treat them as flanked, and assuming the creature hasn't spent any action to realize the illusion isn't real by studying it, I would say no, it is not considered interacting. Its the first part of the wording which says "Creatures encountering an illusion usually do not recieve saving throws" which to me is the biggest indicator.
It would also make that ability entirely pointless if as soon as you use it they could get a saving throw and have it not work.