That's right for the email storage. WLM 2012 stores contacts here : Users\User_Name\AppData\Local\Microsoft\Windows Live\Contacts
Older versions can store them at Users\User_Name\AppData\Local\Microsoft\Windows Live Contacts.
Just to say, I had no problem with contact transfer frow a WLM 2012 (clean install) on Win7 to a WLM 2012 on a Win 10 VM, they're perfectly visible.
An explanation for having blank contacts on new machine would be that WLM 2012 is not the only version that has been on that Win 7 machine. I have never tested this scenario but how could that be if there was let's say WLM 2009 installed a while back, upgraded to WLM 2011 then 2012 ?
If I am right, then
@fincoder's workaround using Nirsoft tool may the best option.