Hi Adrian - Unfortunately this question is almost two years old so I don't know if you've already found a workaround.
The functionality you highlighted is frequently referred to as swimlanes. Unfortunately, as great as the Kanban functionality in Odoo is, it's currently lacking this type of efficiency which is often critical in Agile methodologies.
I've seen on implementation of this type of functionality on Github that also used a direct API link to JIRA project management. However, if you are running Odoo SaaS, then there is not functionality like this available natively or without custom development. Additionally, if you have no need to integrate to external project management like JIRA, then the module is of no use.
One work around my team has used has been to utilize the tagging function and to create a report (from Dashboard view) using a search parameter. You can use a grouping rule that would that group tasks in a column view using your set criteria (such as by user). While this doesn't create the visual cleanliness of what you demonstrated above, it does at least allow individual users to have the ability to quickly breakdown what tasks and projects they are responsible for executing on.
Lastly, another work around (that, admittedly is far more tedious) is to create custom fields within the tasks and projects and to import/export projects into MS Project (2010 or newer) that allow you to manipulate data and views more efficiently. We had one project manager that was ridiculous about only wanting to use MS Project so she went through the task each day of taking what was updated and just exporting data for reports and swimlane views in MS project professional and would sync the csv with Sharepoint.
If you have the staff (and obviously the absolute need), this can be the least technical work aroundthat wouldn't require custom development or dependencies on modules within Odoo. The only reason we found this useful was because it still allowed us to track billables/invoices/time within Odoo against employee while being able to have the flexibility to report as necessary in MS Project.