Destruct is a mostly unnecessary variant of the verb destroy. Derived in the 17th century by backformation from destruction (destroy‘s corresponding noun), destruct had mostly faded from the language by the mid-1900s, when it was revived in rocketry and in the phrases self-destruct and auto-destruct. Outside these uses, destruct can usually give way to destroy.
In rocket science, to destruct means to destroy (a craft) intentionally after launch, usually due to defective performance—for example:
There was no obvious reason to send the destruct signal, since the rotation of the Earth would carry the missile out over the Pacific. [The Space Review]
Because the following examples have nothing to do with science, there’s no reason that destruct should not be changed to destroy (though perhaps the writers feel destruct sounds better):
[H]e has been able to create a team that is built for the long haul, and won’t destruct itself from within. [Fox 11 Online]
The agitated mob not only stopped at this but further went on to destruct the AIR and Doordarshan offices. [Ganpati News]