It still opens the wrong page on Chrome, Opera Mini, and the Silk browser. BTW, I tried clearing the cache on Chrome and Opera, to no avail. I have tried it on another Kindle (a Fire HD 8), with the same result.
It works just fine on my Android phone, opening the TMN Lite Test automatically.
A problem peculiar to Kindles, perhaps?
This morning I tried it on a new Kindle Fire 7, one on which I have not installed Google services. It still does not open the correct page.