How did a user manage to get my multi-window app to run in "Tabbed Windows Mode"?

Just wondering what version of macOS you're running? The other user must be using macOS Sierra, what about you?

In macOS Sierra tabs are supported in any application where it’s possible to have multiple windows open. Based on your description, your app supports multiple simultaneous windows.

Assuming you have macOS Sierra installed, you can activate this in the way you found through your Google search. But if you haven't, then you won't be able to get tabbed windows to work.

If you do have the latest version of macOS Sierra installed, update your question and let me know. I'll see what I can dig up.