I can't download latest Minecraft launcher, only lets me play demo?

I bought Minecraft for my son, and after downloading the launcher - which is NOT the latest version for some reason, its 1.3.7 - it only lets him play demo…
Why can't I download the latest launcher, which is 1.6.something?
Might that be the reason why it only lets him play Demo?
I'm sure we're logging in with the correct email and pw… Still, only Demo… For almost $30… :/