cms or not depends on if they need it. i never try to push anything unless client needs it. ask your client if they would need to add/edit content by themselves.
That particular website is a Wordpress website, so it’s a CMS. I agree with webcosmo, I always will find out if they need control of the website, ability to add photos, edit content, etc.
That first meeting/phone call/email with the client is crucial in sealing the deal. Before discussing pricing or agreements, always find out their needs. Let them speak, ask them questions and find out what they want it to do. Then lock them up in an agreement!
Have been speaking with one of their employees who said they have an IT department who may be able to manage it after sales. But I’m also gauging they will come back to me for repeat business.
A cms would give them some more control. As you know customising templates can be tricky.