The parking lot is one of those gray areas that is not quite public, but not quite private either. By exercising control over an individual's vehicle, the employer is infringing on that individual's privacy. While an employer is not the government, the employment contract does not give the employer the right to interfere in the employee's private affairs, absent a valid interest.
The OK legislature decided that the employee's privacy interest outweighs the employer's theoretical contractual interest in whether or not the employee has a firearm in the car. That's their job.
Actually, no. The right to keep and bear arms shall not be infringed. The First Amendment applies only to Congress. The Second Amendment applies to Congress, the courts, the Executive, the several States, localities, and private properties. A private property owner has no more right to tell you to be unarmed than he would to require you arrive at the property line naked. I'd make exception for naturist resorts private areas, but not even that. The right to keep and bear arms = the right to life. It is not negotiable.