The Zoom Admin should probably work along side the Marketo Admin to enable the integration. The Zoom Admin is only needed to enter the launch point credentials in Zoom. The creation of the Launch Point and Marketo Program will be completed by your Marketo Admin/team.
Good set of instructions can be found here:https://zoomappdocs.docs.stoplight.io/marketo
The Zoom admin does not need access to Marketo for the initial setup. However, if you do plan for them going into Marketo to setup the various events and reporting, then yes they would need access - but not admin.
Please note: Only webinars created by the Zoom admin user will be visible in Marketo, if you have other Zoom users who created webinars, they would need to be added to the integration profile in Zoom.
Hope this helps!