Does the customer need a Zoom account?

Does the customer have to sign up for Zoom in order to have a video meeting with us?

No, the customer doesn't need a Zoom account to have a meeting with you, they can join a meeting with just the meeting invitation.

However, they will be asked to download the Zoom client in order to join the meeting. Zoom doesn't require that they provide any email or account to do this.

If they don't wish to do this, they can join from the browser with limited functionality. 

Zoom offers the customer these choices when they join the meeting: