Dear Daniel,
In any internet browser, go to: https://portal.office.com, access with your Office 365 account (same Teams account), then click on Planner tile, you will see Planner app, or go directly to: https://tasks.office.com/, then in left pane, click on "Planner Hub", you should have the same Plan as in Teams, then open the Plan, and there you will have the ellipsis button, click in there, and select "Export Plan to Excel".
By the way, the screen-capture that you says from Youtube video is from Planner app, is not a Plan inside Teams.
Regards,
Renzo.