Why does the NFL sanction players when there is a legal system that already handles punishment for crimes?

The players are under contract. Part of that contract sets penalties for violation of certain clauses of the contract. It's totally legal.

For instance, let's say I sign a contract for employment with a company. One clause of that contract states that I can be penalized by the company for violating the company code of conduct. Now let's say I embezzle funds from the company and stalk certain female employees. Both of these are criminal offenses, and both would violate company code of conduct.

I could be charged with the applicable crimes and penalized by the company for the contract violations.

They have the power of the purse. These guys work for the NFL indirectly and are subject to the rules/punishment of the NFL.

It's not illegal to tell your boss to go F himself, yet you can be fired for it.

Think about that.