No.

No to what? That corruption is the right word or that it has to be linked to some kind of bribery?

The latter. Consider embezzlement, for instance. That's a case in which a person abuses their position for personal gain without expecting payment from another. Abuse that festers in the wake of successful attempts to frustrate legitimate competition or oversight is also properly regarded as corrupt, since the system intended to prevent it has been (that's right) corrupted.