Yes, it works, but Apple didn’t put too much effort in user friendlyness:

Note: In non-Safari (e.g. Firefox) browser nothing happens when you click the button. You must use Safari directly.

Install process is as follows:

1. You visit the page and click the button.

2. You get a prompt, and need to confirm. You may also not get a prompt.

3. Go to the iOS Settings and below the first section (profile section) there is a button to give permission to a new app store.

4. Then you return to the browser and click the button again, and the app store installs and appears on your home screen.