well it's a mess then, as that page says:
The latest version of the Kindle for PC app can be used on any computer running Windows XP, Windows Vista, Windows 7, Windows 8 or 8.1, or Windows 10 in Desktop Mode.
so it is clearly intended to link to the desktop version. if it doesn't them amazon have screwed up.
I'd go one step better than saving the correct link and save the actual .exe desktop installer for future use.
but actually - i am finding that the link
https://www.amazon.co.uk/kindleforpc
leads to a choice of : download app from store ( that will be the metro version)
or "enter your email " for amazon to send you the download link.
https://www.amazon.co.uk/gp/digital/...ort_kindleapps
( which is the merry go round I recall riding some months back) . if you open that email , once received, on a win 7 PC, and click the link it contains what do you get then ?
I ( a few months back) got the desktop installer...