So I have been struggling with this for a bit, the multiple different options, with only one offering the actual Visio installation and then not being able to select the option that is advertised in this article...
Here is what I found, you do not get the option to buy Visio on a personal account only on a business account, please do not ask me why it is a Microsoft thing.
When you have a business account and you choose to pay for the Visio license that is what you get a Visio license. But that license is not assigned to any of your business users even if there is only a single business user in the organization. So in order to get the option mentioned here you will have to go into the administration portal and assign the license to the user that is supposed to install the Visio application. When that is done, log in as that user and this time you will see the option to install Visio... which by the way downloads the same installer as for the regular Office installation and will check your license with Microsoft just like before this time seeing that you also pay for Visio so it will install this as part of the Office installation.
Please do not ask me why this insanity is required or why Microsoft decided to produce a help document with only half the information required to answer the users questions. It is a very large organization that clearly has better things to do than to help paying users get what they pay for.