The at-will clause in your employment contract is one of MANY terms with rather far-reaching legal implications.

But for example you almost certainly have a moonlighting clause with specific rules. You have invention disclosure and ownership with rules. These represent binding contracts between you and your employer, often with rules around conflict resolution that are also legally binding.

Most jobs require the employee to sign a contract. It's just not a contract that gives them any assurance of keeping their job.