Mojave App Store is only showing Updates tab
I have found the solution (and origin) to this problem. Thanks @charles for giving me the insight. 

The problem occurs because the new Mac App Store app CFBundleVersion is marked as 1 so if you have any copy of the old Mac App Store (which had CFBundleVersion over 459) in the system, macOS will think is the most recent version and will try to use it on the background.

This is why if you go the the Apple Logo > App Store… it tries to open the old version.

Deleting the old app bundle from the system resolves the problem.