The WhatsApp team is working very hard at improving the application for Windows 10 Mobile. After recently updating the app to version 2.16.140, the app has been updated to new version 2.16.142.
Now you can see your contacts Email and DOB in the Profile Info page. Please see the screenshot below for more clarity.
This is a good addition by the team bringing the app to have more detail info of the contact you are chatting with.
Do let us know what do you think about the latest addition to the Beta App in the comments below.