When you log in to the Twitch Dev dashboard, the dashboard you see by default is your personal dashboard. As far as I’m aware it’s not possible to have an organisation without having your own dashboard as you need to have logged in to the Twitch Dev site with a Twitch account.
Even if you create a Twitch account with the name of your organisation, that’s still a personal dashboard and NOT an organisation dashboard which is why it would lack the games tab or any of the other tabs associated with game developers such as game ownership, analytics, drops, etc…