Hey fowlesy! Thanks for reaching out.
The Visio app comes pre-installed in teams and doesn't require any additional install steps. All apps installed for the user in teams are accessible via the 3 dots in the left menu. Pre-installed first party apps are not present on the app store, and hence you can't see the Visio app there. That being said you can definitely search for Visio while adding a tab, and it should pop-up in the results for tab addition as described in the blog.
PS: Visio as a tab is still not available in Gov/Sovereign clouds. So if you belong to any of these clouds, I would request you to hold tight for some time, and we will release these functionalities in gov clouds soon.
I hope this information helps - please feel free to reach out in case you need further clarification.