Hi Cathy,
What you're describing is definitely possible, and a type of sharing security that Workfront is designed to handle. It will definitely take some careful design at the outset, and may require some rework on how your processes are designed for the Marketing team depending on how they were initially set-up.
Sharing within Workfront can be controlled by Company, Group, Team, Role and individual person across all objects (templates, queues, reports etc.)
Taking the Template object as an example, you could have a Template that has Template Sharing set to View for the Video Department Group and Manage for the specific user who designed the template. When a Marketing person said 'Create new project', that template would not appear as long as they were not a member of the Video Department Group. Project Sharing on that template could then be set to View/Contribute/Manage for the Video Department Group only.
At the initial setup of that project, only the Video Dept would be able to see it in search results. If a Marketing person were assigned a specific task on that project, then the sharing settings in Project Preferences in Setup would take hold. You could grant them access to the task and project, or the task only - for example. Those settings can also be controlled BY the Group, so the rules for Marketing don't have to be the rules for Video etc.
The same sort of settings apply across most objects, so it's mostly a matter of carefully storyboarding out sample scenarios and what should happen for each. The hard part in your instance may be going backwards to retrofit this into the existing Marketing processes, depending on how they were setup. It's not impossible, just a lot of testing.
Happy to elaborate if you have specific scenarios in mind.
Katherine