According to the "Contract Law" and other relevant laws and regulations, if it is not affixed with the official seal, it will not have administrative effect in the legal sense. However, in general, companies will not require consistency in administrative effectiveness and legal meaning in specific operations. In other words, within the company, absolutely any contract or the company recognizes the contractual relationship with you. But if a larger problem occurs, involving judicial intervention or litigation, it will be a bit troublesome. The chairman of the board you are talking about is neither the company's legal representative nor the company's chief executive (general manager), so your contract is likely to be deemed invalid and the court may not recognize it.

In fact, many companies operate this way, and the risk is not high. In order to save some financial troubles and reduce some procedures. I personally feel that if you have no enemies in the company, you should be able to rest assured.