If you know happy rich people that don't have a job, you got your counter example, and one is enough.

I do.

People usually need to have a purpose, but it doesn't need to be a job.

I agree "people need a purpose to be happy" is much more digestible than "people need a job to be happy". However, it has to be qualified with "some people need a purpose to be happy". Defining, or worse dictating, happiness for everyone is a fool's errand and, ironically, usually leads to large scale mass murder or starvation.