Do you by any chance have more than one Google account? That might explain that behaviour, if you purchased under one but the browser thinks you're logged in as the other.
I think Google Play is really set up for Android users -- to whom the three-dots thing is a more obvious signifier of menu.
No and yes. No I don't have more than one, but yes other members of my family use this machine occasionally. However: I had to log in to the "correct" account at the start of the process in order to see Google Play (and make my purchase). I would think that once I had done that, it should have handled the rest correctly. Perhaps Google should consider hiring someone who actually uses the internet :-P
Re: Download fails with 404
I think Google Play is really set up for Android users -- to whom the three-dots thing is a more obvious signifier of menu.
Re: Download fails with 404