Hm.. from what I've tried with that installer you linked there, it appears to require the BNET client to install. And by having the BNET client (and afterwards, logging into your BNET account), it doesn't install. So it appears Blizzard now works in even more mysterious ways than before...
EDIT: Yeah, by using that installer, it also prompts me to install the BNET client if I don't already have it installed.
And once it's installed, and after clicking on the Hearthstone Beta Setup.exe, it'll prompt you to log into the BNET client. After logging in, it'll just say "Sorry, but you cannot play this game yet". Blizzard's tricky these days...