Any person or group of persons for whom an employee works or has worked or normally worked or sought to work under a contract of employment.

No, oral or written contracts of service apply equally and are enforceable under the law.

Therefore, the absence of a written contract of employment does not stop any party to enforce it or to fulfil their obligations. 

The only difference is in the means of proving the existence of both

A Contract of Employment  is any agreement whether in writing or verbal, expressed or implied, whereby:

One person agrees to employ another as an employee; and

The other person agrees to serve the employer as an employee in return for remuneration/payment.